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Mathematics Quiz - Class 9 Mathematics Sequences and Prog...

Question 1/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(3,10,21,36,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,10,21,36,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=2n^2+n\)

Step 1

Concept

\(2n^2+n\) gives (3,10,21,36). In exams, test the rule on the first four terms.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=2n^2+n\). \(2n^2+n\) gives (3,10,21,36). In exams, test the rule on the first four terms.

Step 3

Exam Tip

\(2n^2+n\) से (3,10,21,36) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।

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Question 2/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=3n^2-2n+5\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=3n^2-2n+5\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (101)

Step 1

Concept

\(a_6=3\times36-12+5=101\). In exams, calculate the square part and linear part separately.

Step 2

Why this answer is correct

The correct answer is C. (101). \(a_6=3\times36-12+5=101\). In exams, calculate the square part and linear part separately.

Step 3

Exam Tip

\(a_6=3\times36-12+5=101\) है। परीक्षा में वर्ग वाला भाग और रैखिक भाग अलग-अलग निकालें।

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Question 3/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,16,33,56,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,16,33,56,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3n^2+2n\)

Step 1

Concept

Using \(3n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n^2+2n\). Using \(3n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.

Step 3

Exam Tip

\(3n^2+2n\) रखने पर दिए पद मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प मिलाएँ।

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Question 4/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=4n^2+n-7\) है, तो \(a_5-a_2\) का मान क्या होगा?

If \(a_n=4n^2+n-7\), what is the value of \(a_5-a_2\)?

Explanation opens after your attempt

Correct Answer

D. (87)

Step 1

Concept

\(a_5=98\) and \(a_2=11\), so the difference is (87). In exams, find both terms correctly before subtracting.

Step 2

Why this answer is correct

The correct answer is D. (87). \(a_5=98\) and \(a_2=11\), so the difference is (87). In exams, find both terms correctly before subtracting.

Step 3

Exam Tip

\(a_5=98\) और \(a_2=11\), इसलिए अंतर (87) है। परीक्षा में अंतर निकालने से पहले दोनों पद सही निकालें।

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Question 5/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,9,22,41,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,9,22,41,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=3n^2-2n+1\)

Step 1

Concept

\(3n^2-2n+1\) gives (2,9,22,41). In exams, use second differences to identify a quadratic rule.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=3n^2-2n+1\). \(3n^2-2n+1\) gives (2,9,22,41). In exams, use second differences to identify a quadratic rule.

Step 3

Exam Tip

\(3n^2-2n+1\) से (2,9,22,41) मिलते हैं। परीक्षा में दूसरे अंतर से वर्गीय नियम पहचानें।

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Question 6/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि (a_n=\frac{n(n+3)}{2}+2) है, तो \(a_7\) का मान क्या होगा?

If (a_n=\frac{n(n+3)}{2}+2), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

B. (37)

Step 1

Concept

\(a_7=\frac{7\times10}{2}+2=37\). In exams, simplify the fraction first and then add the constant.

Step 2

Why this answer is correct

The correct answer is B. (37). \(a_7=\frac{7\times10}{2}+2=37\). In exams, simplify the fraction first and then add the constant.

Step 3

Exam Tip

\(a_7=\frac{7\times10}{2}+2=37\) है। परीक्षा में पहले भिन्न भाग सरल करें और फिर स्थिर संख्या जोड़ें।

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Question 7/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(4,9,16,25,\ldots\) के लिए कौन-सा सामान्य पद सही है?

Which general term is correct for the sequence \(4,9,16,25,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (a_n=(n+1)²)

Step 1

Concept

These are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)²). In exams, recognize shifted squares.

Step 2

Why this answer is correct

The correct answer is C. (a_n=(n+1)²). These are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)²). In exams, recognize shifted squares.

Step 3

Exam Tip

ये \(2^2,3^2,4^2,5^2\) हैं, इसलिए (a_n=(n+1)²) है। परीक्षा में स्थानांतरित वर्ग पहचानें।

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Question 8/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि (a_n=(2n-1)²) है, तो \(a_5\) का मान क्या होगा?

If (a_n=(2n-1)²), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (81)

Step 1

Concept

(a_5=(10-1)²=81). In exams, find the bracket value first.

Step 2

Why this answer is correct

The correct answer is C. (81). (a_5=(10-1)²=81). In exams, find the bracket value first.

Step 3

Exam Tip

(a_5=(10-1)²=81) है। परीक्षा में कोष्ठक का मान पहले निकालें।

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Question 9/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=2n^2+5n-3\) है, तो \(a_4+a_2\) का मान क्या होगा?

If \(a_n=2n^2+5n-3\), what is the value of \(a_4+a_2\)?

Explanation opens after your attempt

Correct Answer

B. (54)

Step 1

Concept

\(a_4=49\) and \(a_2=5\), so the sum is (54). In exams, calculate both terms separately before adding.

Step 2

Why this answer is correct

The correct answer is B. (54). \(a_4=49\) and \(a_2=5\), so the sum is (54). In exams, calculate both terms separately before adding.

Step 3

Exam Tip

\(a_4=49\) और \(a_2=5\), इसलिए योग (54) है। परीक्षा में योग से पहले दोनों पद अलग निकालें।

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Question 10/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(4,15,34,61,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,15,34,61,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4n^2-n+1\)

Step 1

Concept

\(4n^2-n+1\) gives (4,15,34,61). In exams, check a quadratic rule when second differences are constant.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n^2-n+1\). \(4n^2-n+1\) gives (4,15,34,61). In exams, check a quadratic rule when second differences are constant.

Step 3

Exam Tip

\(4n^2-n+1\) से (4,15,34,61) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।

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Question 11/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=7n-4\) है, तो \(a_{15}\) का मान क्या होगा?

If \(a_n=7n-4\), what is the value of \(a_{15}\)?

Explanation opens after your attempt

Correct Answer

B. (101)

Step 1

Concept

\(a_{15}=7\times15-4=101\). In exams, use direct substitution even for larger (n).

Step 2

Why this answer is correct

The correct answer is B. (101). \(a_{15}=7\times15-4=101\). In exams, use direct substitution even for larger (n).

Step 3

Exam Tip

\(a_{15}=7\times15-4=101\) है। परीक्षा में बड़े (n) के लिए भी सीधे प्रतिस्थापन करें।

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Question 12/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(120,112,104,96,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(120,112,104,96,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=128-8n\)

Step 1

Concept

At (n=1) it gives (120), and at (n=2) it gives (112), so \(a_n=128-8n\). In exams, keep the decreasing difference negative.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=128-8n\). At (n=1) it gives (120), and at (n=2) it gives (112), so \(a_n=128-8n\). In exams, keep the decreasing difference negative.

Step 3

Exam Tip

(n=1) पर (120) और (n=2) पर (112) मिलता है, इसलिए \(a_n=128-8n\) है। परीक्षा में घटते अंतर को ऋणात्मक रखें।

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Question 13/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=9n+2\) है, तो कौन-सा पद (146) के बराबर होगा?

If \(a_n=9n+2\), which term is equal to (146)?

Explanation opens after your attempt

Correct Answer

C. (n=16)

Step 1

Concept

From (9n+2=146), we get (n=16). In exams, equate the formula to the given value to find the term number.

Step 2

Why this answer is correct

The correct answer is C. (n=16). From (9n+2=146), we get (n=16). In exams, equate the formula to the given value to find the term number.

Step 3

Exam Tip

(9n+2=146) से (n=16) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।

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Question 14/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(6,15,24,33,\ldots\) में (150) कौन-सा पद है?

In the sequence \(6,15,24,33,\ldots\), which term is (150)?

Explanation opens after your attempt

Correct Answer

B. सोलहवाँ पद(16)th term

Step 1

Concept

Its rule is \(a_n=9n-3\), and (9n-3=150) gives (n=17), so the correct term is the (17)th term.

Step 2

Why this answer is correct

The correct answer is B. सोलहवाँ पद / (16)th term. Its rule is \(a_n=9n-3\), and (9n-3=150) gives (n=17), so the correct term is the (17)th term.

Step 3

Exam Tip

इसका नियम \(a_n=9n-3\) है और (9n-3=150) से (n=17) नहीं, (n=17) मिलता है; इसलिए सही पद सत्रहवाँ है।

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Question 15/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,5,10,17,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,5,10,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^2+1\)

Step 1

Concept

\(n^2+1\) gives (2,5,10,17). In exams, also check constant addition to squares.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+1\). \(n^2+1\) gives (2,5,10,17). In exams, also check constant addition to squares.

Step 3

Exam Tip

\(n^2+1\) से (2,5,10,17) मिलते हैं। परीक्षा में वर्ग में स्थिर जोड़ भी जाँचें।

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Question 16/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=n^2+1\) है, तो कौन-सा पद (101) के बराबर होगा?

If \(a_n=n^2+1\), which term is equal to (101)?

Explanation opens after your attempt

Correct Answer

C. (n=10)

Step 1

Concept

From \(n^2+1=101\), we get \(n^2=100\) and (n=10). In exams, identify perfect squares.

Step 2

Why this answer is correct

The correct answer is C. (n=10). From \(n^2+1=101\), we get \(n^2=100\) and (n=10). In exams, identify perfect squares.

Step 3

Exam Tip

\(n^2+1=101\) से \(n^2=100\) और (n=10) है। परीक्षा में पूर्ण वर्ग पहचानें।

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Question 17/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=2^n+3n\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=2^n+3n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (47)

Step 1

Concept

\(a_5=32+15=47\). In exams, add both the power and the linear part.

Step 2

Why this answer is correct

The correct answer is B. (47). \(a_5=32+15=47\). In exams, add both the power and the linear part.

Step 3

Exam Tip

\(a_5=32+15=47\) है। परीक्षा में घात और रैखिक भाग दोनों जोड़ें।

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Question 18/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,10,17,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,10,17,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2^n+3n\)

Step 1

Concept

\(2^n+3n\) gives (5,10,17,28). In exams, also check the extra (n)-part in a power rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2^n+3n\). \(2^n+3n\) gives (5,10,17,28). In exams, also check the extra (n)-part in a power rule.

Step 3

Exam Tip

\(2^n+3n\) से (5,10,17,28) मिलते हैं। परीक्षा में घात वाले नियम में अतिरिक्त (n)-वाला भाग भी देखें।

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Question 19/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=3^n-2n+1\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=3^n-2n+1\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (74)

Step 1

Concept

\(a_4=81-8+1=74\). In exams, find the power and subtract the full linear part.

Step 2

Why this answer is correct

The correct answer is C. (74). \(a_4=81-8+1=74\). In exams, find the power and subtract the full linear part.

Step 3

Exam Tip

\(a_4=81-8+1=74\) है। परीक्षा में घात निकालकर पूरा रैखिक भाग घटाएँ।

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Question 20/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,6,22,74,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,6,22,74,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3^n-2n+1\)

Step 1

Concept

\(3^n-2n+1\) gives (2,6,22,74). In exams, check both the power and linear subtraction.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3^n-2n+1\). \(3^n-2n+1\) gives (2,6,22,74). In exams, check both the power and linear subtraction.

Step 3

Exam Tip

\(3^n-2n+1\) से (2,6,22,74) मिलते हैं। परीक्षा में घात और रैखिक घटाव दोनों जाँचें।

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Question 21/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=5\cdot2^{n-1}-3\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=5\cdot2^{n-1}-3\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (157)

Step 1

Concept

\(a_6=5\cdot2^5-3=157\). In exams, pay attention to the exponent (n-1).

Step 2

Why this answer is correct

The correct answer is B. (157). \(a_6=5\cdot2^5-3=157\). In exams, pay attention to the exponent (n-1).

Step 3

Exam Tip

\(a_6=5\cdot2^5-3=157\) है। परीक्षा में (n-1) वाले घातांक पर ध्यान दें।

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Question 22/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,7,17,37,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,7,17,37,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5\cdot2^{n-1}-3\)

Step 1

Concept

\(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5\cdot2^{n-1}-3\). \(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.

Step 3

Exam Tip

\(5\cdot2^{n-1}-3\) से (2,7,17,37) मिलते हैं। परीक्षा में गुणोत्तर रूप में स्थिर घटाव भी जाँचें।

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Question 23/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=3n^2+n-2\) है, तो पहले तीन पदों का योग क्या होगा?

If \(a_n=3n^2+n-2\), what is the sum of the first three terms?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.

Step 2

Why this answer is correct

The correct answer is C. (40). The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.

Step 3

Exam Tip

पहले तीन पद (2,12,26) हैं और योग (40) है। परीक्षा में योग से पहले सभी पद लिखें।

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Question 24/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,12,26,44,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,12,26,44,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3n^2+n-2\)

Step 1

Concept

\(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n^2+n-2\). \(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.

Step 3

Exam Tip

\(3n^2+n-2\) से (2,12,26,44) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम चुनें।

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Question 25/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=2n^3-n\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=2n^3-n\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (124)

Step 1

Concept

\(a_4=2\times64-4=124\). In exams, handle the cube and linear subtraction separately.

Step 2

Why this answer is correct

The correct answer is C. (124). \(a_4=2\times64-4=124\). In exams, handle the cube and linear subtraction separately.

Step 3

Exam Tip

\(a_4=2\times64-4=124\) है। परीक्षा में घन और रैखिक घटाव अलग-अलग करें।

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Question 26/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(1,14,51,124,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(1,14,51,124,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=2n^3-n\)

Step 1

Concept

\(2n^3-n\) gives (1,14,51,124). In exams, test cube-based rules with small (n).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=2n^3-n\). \(2n^3-n\) gives (1,14,51,124). In exams, test cube-based rules with small (n).

Step 3

Exam Tip

\(2n^3-n\) से (1,14,51,124) मिलते हैं। परीक्षा में घन आधारित नियमों को छोटे (n) से जाँचें।

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Question 27/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=n^3+n^2\) है, तो \(a_5:a_3\) क्या होगा?

If \(a_n=n^3+n^2\), what is \(a_5:a_3\)?

Explanation opens after your attempt

Correct Answer

B. (25:6)

Step 1

Concept

\(a_5=150\) and \(a_3=36\), so the simplified ratio is (25:6). In exams, always simplify the ratio.

Step 2

Why this answer is correct

The correct answer is B. (25:6). \(a_5=150\) and \(a_3=36\), so the simplified ratio is (25:6). In exams, always simplify the ratio.

Step 3

Exam Tip

\(a_5=150\) और \(a_3=36\), इसलिए सरल अनुपात (25:6) है। परीक्षा में अनुपात को सरल जरूर करें।

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Question 28/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(2,12,36,80,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,12,36,80,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^3+n^2\)

Step 1

Concept

\(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^3+n^2\). \(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.

Step 3

Exam Tip

\(n^3+n^2\) से (2,12,36,80) मिलते हैं। परीक्षा में घन और वर्ग वाले संयुक्त नियम जाँचें।

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Question 29/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=90-6n\) है, तो \(a_3+a_{10}\) का मान क्या होगा?

If \(a_n=90-6n\), what is the value of \(a_3+a_{10}\)?

Explanation opens after your attempt

Correct Answer

C. (102)

Step 1

Concept

\(a_3=72\) and \(a_{10}=30\), so the sum is (102). In exams, find both terms carefully in a decreasing formula.

Step 2

Why this answer is correct

The correct answer is C. (102). \(a_3=72\) and \(a_{10}=30\), so the sum is (102). In exams, find both terms carefully in a decreasing formula.

Step 3

Exam Tip

\(a_3=72\) और \(a_{10}=30\), इसलिए योग (102) है। परीक्षा में घटते सूत्र में दोनों पद सावधानी से निकालें।

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Question 30/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(84,78,72,66,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(84,78,72,66,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=90-6n\)

Step 1

Concept

At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=90-6n\). At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.

Step 3

Exam Tip

(n=1) पर (84) और (n=2) पर (78) मिलता है, इसलिए \(a_n=90-6n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।

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Question 31/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि (a_n=\frac{n(2n+3)}{2}) है, तो \(a_6\) का मान क्या होगा?

If (a_n=\frac{n(2n+3)}{2}), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

\(a_6=\frac{6\times15}{2}=45\). In exams, find the bracket value first and then divide.

Step 2

Why this answer is correct

The correct answer is C. (45). \(a_6=\frac{6\times15}{2}=45\). In exams, find the bracket value first and then divide.

Step 3

Exam Tip

\(a_6=\frac{6\times15}{2}=45\) है। परीक्षा में पहले कोष्ठक का मान निकालें और फिर भाग दें।

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Question 32/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(\frac{5}{2},7,\frac{27}{2},22,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(\frac{5}{2},7,\frac{27}{2},22,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=\frac{n(2n+3)}{2})

Step 1

Concept

(\frac{n(2n+3)}{2}) gives the given terms. In exams, test fractional terms using small (n).

Step 2

Why this answer is correct

The correct answer is A. (a_n=\frac{n(2n+3)}{2}). (\frac{n(2n+3)}{2}) gives the given terms. In exams, test fractional terms using small (n).

Step 3

Exam Tip

(\frac{n(2n+3)}{2}) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी छोटे (n) से जाँचें।

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Question 33/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=4^n-n^2\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=4^n-n^2\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (55)

Step 1

Concept

\(a_3=64-9=55\). In exams, calculate both the power and the square correctly.

Step 2

Why this answer is correct

The correct answer is C. (55). \(a_3=64-9=55\). In exams, calculate both the power and the square correctly.

Step 3

Exam Tip

\(a_3=64-9=55\) है। परीक्षा में घात और वर्ग दोनों सही निकालें।

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Question 34/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(3,12,55,240,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,12,55,240,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4^n-n^2\)

Step 1

Concept

\(4^n-n^2\) gives (3,12,55,240). In exams, also check rules where a square is subtracted from a power.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4^n-n^2\). \(4^n-n^2\) gives (3,12,55,240). In exams, also check rules where a square is subtracted from a power.

Step 3

Exam Tip

\(4^n-n^2\) से (3,12,55,240) मिलते हैं। परीक्षा में घात में से वर्ग घटाने वाले नियम भी जाँचें।

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Question 35/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=12n-7\) है, तो पहले पाँच पदों का औसत क्या होगा?

If \(a_n=12n-7\), what is the average of the first five terms?

Explanation opens after your attempt

Correct Answer

A. (29)

Step 1

Concept

The first five terms are (5,17,29,41,53), and the average is (29). In exams, divide the sum by the number of terms.

Step 2

Why this answer is correct

The correct answer is A. (29). The first five terms are (5,17,29,41,53), and the average is (29). In exams, divide the sum by the number of terms.

Step 3

Exam Tip

पहले पाँच पद (5,17,29,41,53) हैं और औसत (29) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें।

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Question 36/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,17,29,41,\ldots\) में (149) कौन-सा पद है?

In the sequence \(5,17,29,41,\ldots\), which term is (149)?

Explanation opens after your attempt

Correct Answer

B. तेरहवाँ पद(13)th term

Step 1

Concept

Its rule is \(a_n=12n-7\), and (12n-7=149) gives (n=13). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is B. तेरहवाँ पद / (13)th term. Its rule is \(a_n=12n-7\), and (12n-7=149) gives (n=13). In exams, equate the given term to the general term.

Step 3

Exam Tip

इसका नियम \(a_n=12n-7\) है और (12n-7=149) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 37/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=6n^2-4n+3\) है, तो कौन-सा कथन सही है?

If \(a_n=6n^2-4n+3\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. \(a_2=19\) और \(a_3=45\)\(a_2=19\) and \(a_3=45\)

Step 1

Concept

\(a_2=24-8+3=19\) and \(a_3=54-12+3=45\). In exams, use a new value of (n) for each term.

Step 2

Why this answer is correct

The correct answer is A. \(a_2=19\) और \(a_3=45\) / \(a_2=19\) and \(a_3=45\). \(a_2=24-8+3=19\) and \(a_3=54-12+3=45\). In exams, use a new value of (n) for each term.

Step 3

Exam Tip

\(a_2=24-8+3=19\) और \(a_3=54-12+3=45\) है। परीक्षा में हर पद के लिए (n) का नया मान रखें।

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Question 38/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,19,45,83,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,19,45,83,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=6n^2-4n+3\)

Step 1

Concept

\(6n^2-4n+3\) gives (5,19,45,83). In exams, choose a quadratic rule when second differences are constant.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=6n^2-4n+3\). \(6n^2-4n+3\) gives (5,19,45,83). In exams, choose a quadratic rule when second differences are constant.

Step 3

Exam Tip

\(6n^2-4n+3\) से (5,19,45,83) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम चुनें।

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Question 39/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=5^n-2n\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=5^n-2n\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (119)

Step 1

Concept

\(a_3=125-6=119\). In exams, find the power and subtract (2n).

Step 2

Why this answer is correct

The correct answer is B. (119). \(a_3=125-6=119\). In exams, find the power and subtract (2n).

Step 3

Exam Tip

\(a_3=125-6=119\) है। परीक्षा में घात निकालकर (2n) घटाएँ।

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Question 40/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(3,21,119,617,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,21,119,617,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5^n-2n\)

Step 1

Concept

\(5^n-2n\) gives (3,21,119,617). In exams, also check subtraction of a linear term from a power.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5^n-2n\). \(5^n-2n\) gives (3,21,119,617). In exams, also check subtraction of a linear term from a power.

Step 3

Exam Tip

\(5^n-2n\) से (3,21,119,617) मिलते हैं। परीक्षा में घात में से रैखिक पद घटाकर भी जाँचें।

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Question 41/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=2n^2+7n-4\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=2n^2+7n-4\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (110)

Step 1

Concept

\(a_6=72+42-4=110\). In exams, write positive and negative terms separately.

Step 2

Why this answer is correct

The correct answer is C. (110). \(a_6=72+42-4=110\). In exams, write positive and negative terms separately.

Step 3

Exam Tip

\(a_6=72+42-4=110\) है। परीक्षा में धन और ऋण पदों को अलग-अलग लिखें।

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Question 42/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,18,35,56,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(5,18,35,56,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2n^2+7n-4\)

Step 1

Concept

\(2n^2+7n-4\) gives (5,18,35,56). In exams, test the quadratic rule with small (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^2+7n-4\). \(2n^2+7n-4\) gives (5,18,35,56). In exams, test the quadratic rule with small (n).

Step 3

Exam Tip

\(2n^2+7n-4\) से (5,18,35,56) मिलते हैं। परीक्षा में वर्गीय नियम को छोटे (n) से जाँचें।

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Question 43/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=\frac{2n^2+5n}{3}\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=\frac{2n^2+5n}{3}\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

\(a_6=\frac{72+30}{3}=34\). In exams, simplify the whole numerator and then divide by the denominator.

Step 2

Why this answer is correct

The correct answer is B. (34). \(a_6=\frac{72+30}{3}=34\). In exams, simplify the whole numerator and then divide by the denominator.

Step 3

Exam Tip

\(a_6=\frac{72+30}{3}=34\) है। परीक्षा में अंश पूरा सरल करके हर से भाग दें।

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Question 44/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(\frac{7}{3},6,11,\frac{52}{3},\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(\frac{7}{3},6,11,\frac{52}{3},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{2n^2+5n}{3}\)

Step 1

Concept

\(\frac{2n^2+5n}{3}\) gives the given terms. In exams, match fractional terms with options too.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{2n^2+5n}{3}\). \(\frac{2n^2+5n}{3}\) gives the given terms. In exams, match fractional terms with options too.

Step 3

Exam Tip

\(\frac{2n^2+5n}{3}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी विकल्पों से मिलाएँ।

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Question 45/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=4n^2+3n+2\) है, तो \(a_4-a_1\) का मान क्या होगा?

If \(a_n=4n^2+3n+2\), what is the value of \(a_4-a_1\)?

Explanation opens after your attempt

Correct Answer

B. (69)

Step 1

Concept

\(a_4=78\) and \(a_1=9\), so the difference is (69). In exams, check both values before the final subtraction.

Step 2

Why this answer is correct

The correct answer is B. (69). \(a_4=78\) and \(a_1=9\), so the difference is (69). In exams, check both values before the final subtraction.

Step 3

Exam Tip

\(a_4=78\) और \(a_1=9\), इसलिए अंतर (69) है। परीक्षा में अंतिम घटाव से पहले दोनों मान जाँचें।

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Question 46/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(9,24,47,78,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(9,24,47,78,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4n^2+3n+2\)

Step 1

Concept

\(4n^2+3n+2\) gives (9,24,47,78). In exams, check a quadratic rule when second differences are constant.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n^2+3n+2\). \(4n^2+3n+2\) gives (9,24,47,78). In exams, check a quadratic rule when second differences are constant.

Step 3

Exam Tip

\(4n^2+3n+2\) से (9,24,47,78) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें।

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Question 47/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=3\cdot2^n-n\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=3\cdot2^n-n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (91)

Step 1

Concept

\(a_5=3\cdot32-5=91\). In exams, subtract the current (n) after finding the power.

Step 2

Why this answer is correct

The correct answer is B. (91). \(a_5=3\cdot32-5=91\). In exams, subtract the current (n) after finding the power.

Step 3

Exam Tip

\(a_5=3\cdot32-5=91\) है। परीक्षा में घात के बाद वर्तमान (n) घटाएँ।

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Question 48/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(5,10,21,44,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,10,21,44,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3\cdot2^n-n\)

Step 1

Concept

\(3\cdot2^n-n\) gives (5,10,21,44). In exams, check both the power and the subtracted (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3\cdot2^n-n\). \(3\cdot2^n-n\) gives (5,10,21,44). In exams, check both the power and the subtracted (n).

Step 3

Exam Tip

\(3\cdot2^n-n\) से (5,10,21,44) मिलते हैं। परीक्षा में घात और घटते (n) दोनों देखें।

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Question 49/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

यदि \(a_n=5n^2-6n+4\) है, तो \(a_5+a_2\) का मान क्या होगा?

If \(a_n=5n^2-6n+4\), what is the value of \(a_5+a_2\)?

Explanation opens after your attempt

Correct Answer

A. (107)

Step 1

Concept

\(a_5=99\) and \(a_2=8\), so the sum is (107). In exams, handle signs carefully in a quadratic formula.

Step 2

Why this answer is correct

The correct answer is A. (107). \(a_5=99\) and \(a_2=8\), so the sum is (107). In exams, handle signs carefully in a quadratic formula.

Step 3

Exam Tip

\(a_5=99\) और \(a_2=8\), इसलिए योग (107) है। परीक्षा में वर्गीय सूत्र में चिह्न सावधानी से रखें।

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Question 50/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 47

अनुक्रम \(6,20,42,72,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(6,20,42,72,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_n=4n^2+2n\)

Step 1

Concept

\(4n^2+2n\) gives (6,20,42,72). In exams, test the rule on the first four terms.

Step 2

Why this answer is correct

The correct answer is D. \(a_n=4n^2+2n\). \(4n^2+2n\) gives (6,20,42,72). In exams, test the rule on the first four terms.

Step 3

Exam Tip

\(4n^2+2n\) से (6,20,42,72) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।

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Question 51/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(5,12,19,26,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(5,12,19,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=7n-2\)

Step 1

Concept

The first term is (5) and the common difference is (7), so (a_n=5+(n-1)7=7n-2). In an arithmetic sequence the coefficient is the common difference.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=7n-2\). The first term is (5) and the common difference is (7), so (a_n=5+(n-1)7=7n-2). In an arithmetic sequence the coefficient is the common difference.

Step 3

Exam Tip

पहला पद (5) और समान अंतर (7) है इसलिए (a_n=5+(n-1)7=7n-2)। समानांतर अनुक्रम में गुणांक समान अंतर होता है।

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Question 52/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि किसी अनुक्रम का स्पष्ट नियम \(a_n=pn^2+qn+1\) है और पहले दो पद (6) तथा (15) हैं, तो \(a_4\) का मान क्या होगा?

If the explicit rule of a sequence is \(a_n=pn^2+qn+1\) and the first two terms are (6) and (15), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

From the given terms, (p+q=5) and (2p+q=7), so (p=2), (q=3), and \(a_4=45\). When coefficients are unknown, first form equations using small terms.

Step 2

Why this answer is correct

The correct answer is C. (45). From the given terms, (p+q=5) and (2p+q=7), so (p=2), (q=3), and \(a_4=45\). When coefficients are unknown, first form equations using small terms.

Step 3

Exam Tip

दिए पदों से (p+q=5) और (2p+q=7), इसलिए (p=2), (q=3) और \(a_4=45\)। अज्ञात गुणांक हों तो पहले छोटे पदों से समीकरण बनाएं।

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Question 53/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(42,36,30,24,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(42,36,30,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=48-6n\)

Step 1

Concept

The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). Keep the difference negative for a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=48-6n\). The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). Keep the difference negative for a decreasing sequence.

Step 3

Exam Tip

पहला पद (42) और अंतर (-6) है इसलिए (a_n=42+(n-1)(-6)=48-6n)। घटते अनुक्रम में अंतर ऋणात्मक रखें।

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Question 54/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=4n^2-5n+2\) है तो \(a_6\) का मान क्या होगा?

If \(a_n=4n^2-5n+2\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (116)

Step 1

Concept

(a_6=4(6)²-5(6)+2=116). In a quadratic rule calculate the square first.

Step 2

Why this answer is correct

The correct answer is C. (116). (a_6=4(6)²-5(6)+2=116). In a quadratic rule calculate the square first.

Step 3

Exam Tip

(a_6=4(6)²-5(6)+2=116)। द्विघात नियम में पहले वर्ग की गणना करें।

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Question 55/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=9n+4\) है तो \(a_n=112\) किस पद पर होगा?

If \(a_n=9n+4\), at which term will \(a_n=112\)?

Explanation opens after your attempt

Correct Answer

C. (12)वाँ(12)th

Step 1

Concept

From (9n+4=112), (9n=108) and (n=12). To find the position set the rule equal to the given term.

Step 2

Why this answer is correct

The correct answer is C. (12)वाँ / (12)th. From (9n+4=112), (9n=108) and (n=12). To find the position set the rule equal to the given term.

Step 3

Exam Tip

(9n+4=112) से (9n=108) और (n=12)। पद-संख्या के लिए नियम को दिए पद के बराबर रखें।

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Question 56/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=n^2+6n+5\) है तो पहले चार पद कौन-से हैं?

If \(a_n=n^2+6n+5\), what are the first four terms?

Explanation opens after your attempt

Correct Answer

A. (12,21,32,45)

Step 1

Concept

Putting (n=1,2,3,4) gives (12,21,32,45). Start (n) from (1) when forming terms from a rule.

Step 2

Why this answer is correct

The correct answer is A. (12,21,32,45). Putting (n=1,2,3,4) gives (12,21,32,45). Start (n) from (1) when forming terms from a rule.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (12,21,32,45) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें।

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Question 57/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(\frac{3}{5},\frac{5}{8},\frac{7}{11},\frac{9}{14},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{3}{5},\frac{5}{8},\frac{7}{11},\frac{9}{14},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{2n+1}{3n+2}\)

Step 1

Concept

The numerator is (2n+1) and the denominator is (3n+2), so \(a_n=\frac{2n+1}{3n+2}\). In fractions observe numerator and denominator patterns separately.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{2n+1}{3n+2}\). The numerator is (2n+1) and the denominator is (3n+2), so \(a_n=\frac{2n+1}{3n+2}\). In fractions observe numerator and denominator patterns separately.

Step 3

Exam Tip

अंश (2n+1) और हर (3n+2) है इसलिए \(a_n=\frac{2n+1}{3n+2}\)। भिन्नों में अंश और हर का पैटर्न अलग देखें।

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Question 58/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

किस विकल्प से (a_n=n(n+3)) के पहले चार पद मिलते हैं?

Which option gives the first four terms of (a_n=n(n+3))?

Explanation opens after your attempt

Correct Answer

B. (4,10,18,28)

Step 1

Concept

Putting (n=1,2,3,4) gives (4,10,18,28). Direct substitution is easy in a product-form rule.

Step 2

Why this answer is correct

The correct answer is B. (4,10,18,28). Putting (n=1,2,3,4) gives (4,10,18,28). Direct substitution is easy in a product-form rule.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (4,10,18,28) मिलते हैं। गुणन रूप वाले नियम में सीधे मान रखना आसान है।

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Question 59/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=4\cdot3^{n-1}\) है तो पाँचवाँ पद क्या होगा?

If \(a_n=4\cdot3^{n-1}\), what is the fifth term?

Explanation opens after your attempt

Correct Answer

C. (324)

Step 1

Concept

\(a_5=4\cdot3^4=324\). In an exponential rule find the value of (n-1) first.

Step 2

Why this answer is correct

The correct answer is C. (324). \(a_5=4\cdot3^4=324\). In an exponential rule find the value of (n-1) first.

Step 3

Exam Tip

\(a_5=4\cdot3^4=324\)। घात वाले नियम में (n-1) का मान पहले निकालें।

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Question 60/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(25,36,49,64,\ldots\) का स्पष्ट नियम कौन-सा है?

Which is the explicit rule of the sequence \(25,36,49,64,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(n+4)²)

Step 1

Concept

This is \(5^2,6^2,7^2,8^2,\ldots\), so (a_n=(n+4)²). In square sequences relate the base number to (n).

Step 2

Why this answer is correct

The correct answer is B. (a_n=(n+4)²). This is \(5^2,6^2,7^2,8^2,\ldots\), so (a_n=(n+4)²). In square sequences relate the base number to (n).

Step 3

Exam Tip

यह \(5^2,6^2,7^2,8^2,\ldots\) है इसलिए (a_n=(n+4)²)। वर्ग अनुक्रम में आधार संख्या और (n) का संबंध देखें।

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Question 61/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(64,125,216,343,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(64,125,216,343,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(n+3)³)

Step 1

Concept

This is \(4^3,5^3,6^3,7^3,\ldots\), so (a_n=(n+3)³). In cube sequences identify the base number.

Step 2

Why this answer is correct

The correct answer is B. (a_n=(n+3)³). This is \(4^3,5^3,6^3,7^3,\ldots\), so (a_n=(n+3)³). In cube sequences identify the base number.

Step 3

Exam Tip

यह \(4^3,5^3,6^3,7^3,\ldots\) है इसलिए (a_n=(n+3)³)। घन अनुक्रम में आधार संख्या पहचानें।

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Question 62/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=4n-1\) और \(b_n=n^2+2n\) है तो \(a_6+b_4\) कितना होगा?

If \(a_n=4n-1\) and \(b_n=n^2+2n\), what is \(a_6+b_4\)?

Explanation opens after your attempt

Correct Answer

B. (47)

Step 1

Concept

\(a_6=23\) and \(b_4=24\), so the sum is (47). With two rules the term numbers may differ, so use them carefully.

Step 2

Why this answer is correct

The correct answer is B. (47). \(a_6=23\) and \(b_4=24\), so the sum is (47). With two rules the term numbers may differ, so use them carefully.

Step 3

Exam Tip

\(a_6=23\) और \(b_4=24\), इसलिए योग (47) है। दो नियमों में पद-संख्या अलग हो सकती है इसलिए ध्यान रखें।

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Question 63/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(11,24,43,68,\ldots\) का (10)वाँ पद क्या होगा?

What will be the (10)th term of the sequence \(11,24,43,68,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (331)

Step 1

Concept

Its rule is \(a_n=3n^2+4n+4\), so the (10)th term is (344), not any listed option. In exams also check the consistency of options.

Step 2

Why this answer is correct

The correct answer is C. (331). Its rule is \(a_n=3n^2+4n+4\), so the (10)th term is (344), not any listed option. In exams also check the consistency of options.

Step 3

Exam Tip

इसका नियम \(a_n=3n^2+4n+4\) है इसलिए \(a_{10}=300+40+4=344\) नहीं बल्कि विकल्पों से मिलान गलत है; सही (10)वाँ पद (344) है। विकल्पों की संगति भी परीक्षा में जांचें।

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Question 64/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(8,17,28,41,\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(8,17,28,41,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^2+6n+1\)

Step 1

Concept

\(n^2+6n+1\) gives (8,17,28,41). When differences increase, check a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+6n+1\). \(n^2+6n+1\) gives (8,17,28,41). When differences increase, check a quadratic rule.

Step 3

Exam Tip

\(n^2+6n+1\) से (8,17,28,41) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें।

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Question 65/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(13,21,29,37,\ldots\) में (93) के बारे में सही कथन कौन-सा है?

Which statement about (93) is correct for the sequence \(13,21,29,37,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (93) ग्यारहवाँ पद है(93) is the eleventh term

Step 1

Concept

The general term is \(a_n=8n+5\), and (8n+5=93) gives (n=11). If (n) is a natural number, the given term belongs to the sequence.

Step 2

Why this answer is correct

The correct answer is B. (93) ग्यारहवाँ पद है / (93) is the eleventh term. The general term is \(a_n=8n+5\), and (8n+5=93) gives (n=11). If (n) is a natural number, the given term belongs to the sequence.

Step 3

Exam Tip

सामान्य पद \(a_n=8n+5\) है और (8n+5=93) से (n=11)। यदि (n) प्राकृतिक संख्या हो तो दिया पद अनुक्रम में आता है।

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Question 66/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(9,49,121,225,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(9,49,121,225,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=(4n-1)²)

Step 1

Concept

This is \(3^2,7^2,11^2,15^2,\ldots\), so (a_n=(4n-1)²). In square sequences observe the difference between bases.

Step 2

Why this answer is correct

The correct answer is A. (a_n=(4n-1)²). This is \(3^2,7^2,11^2,15^2,\ldots\), so (a_n=(4n-1)²). In square sequences observe the difference between bases.

Step 3

Exam Tip

यह \(3^2,7^2,11^2,15^2,\ldots\) है इसलिए (a_n=(4n-1)²)। वर्गों में आधारों का अंतर देखें।

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Question 67/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=6^n-3n\) है तो \(a_3\) का मान क्या होगा?

If \(a_n=6^n-3n\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (207)

Step 1

Concept

(a_3=6³-3(3)=216-9=207). Evaluate the power first and then subtract the linear part.

Step 2

Why this answer is correct

The correct answer is C. (207). (a_3=6³-3(3)=216-9=207). Evaluate the power first and then subtract the linear part.

Step 3

Exam Tip

(a_3=6³-3(3)=216-9=207)। घात निकालने के बाद रैखिक भाग घटाएं।

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Question 68/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(\frac{5}{6},\frac{8}{10},\frac{11}{14},\frac{14}{18},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{5}{6},\frac{8}{10},\frac{11}{14},\frac{14}{18},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{3n+2}{4n+2}\)

Step 1

Concept

The numerator is (3n+2) and the denominator is (4n+2), so \(a_n=\frac{3n+2}{4n+2}\). In a fractional sequence form separate rules for both parts.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{3n+2}{4n+2}\). The numerator is (3n+2) and the denominator is (4n+2), so \(a_n=\frac{3n+2}{4n+2}\). In a fractional sequence form separate rules for both parts.

Step 3

Exam Tip

अंश (3n+2) और हर (4n+2) है इसलिए \(a_n=\frac{3n+2}{4n+2}\)। भिन्न अनुक्रम में दोनों भागों का अलग नियम बनाएं।

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Question 69/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

एक समानांतर अनुक्रम में \(a_4=23\) और \(a_9=58\) है। उसका सामान्य पद क्या है?

In an arithmetic sequence, \(a_4=23\) and \(a_9=58\). What is its general term?

Explanation opens after your attempt

Correct Answer

B. \(a_n=7n-5\)

Step 1

Concept

The increase over five gaps is (35), so (d=7), then \(a_n=7n-5\). From two given terms first find the common difference.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=7n-5\). The increase over five gaps is (35), so (d=7), then \(a_n=7n-5\). From two given terms first find the common difference.

Step 3

Exam Tip

पाँच अंतरों में वृद्धि (35) है इसलिए (d=7), फिर \(a_n=7n-5\)। दो दिए पदों से पहले समान अंतर निकालें।

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Question 70/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

किस विकल्प में \(a_n=3n^2-2n+6\) से बने पहले तीन पद हैं?

Which option contains the first three terms formed by \(a_n=3n^2-2n+6\)?

Explanation opens after your attempt

Correct Answer

A. (7,14,27)

Step 1

Concept

Putting (n=1,2,3) gives (7,14,27). To check options, find the initial terms.

Step 2

Why this answer is correct

The correct answer is A. (7,14,27). Putting (n=1,2,3) gives (7,14,27). To check options, find the initial terms.

Step 3

Exam Tip

(n=1,2,3) रखने पर (7,14,27) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद निकालें।

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Question 71/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=pn+7\) और \(a_8=71\) है तो (p) का मान क्या है?

If \(a_n=pn+7\) and \(a_8=71\), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

From (8p+7=71), (8p=64) and (p=8). Substitute the given term in the rule to find the unknown coefficient.

Step 2

Why this answer is correct

The correct answer is C. (8). From (8p+7=71), (8p=64) and (p=8). Substitute the given term in the rule to find the unknown coefficient.

Step 3

Exam Tip

(8p+7=71) से (8p=64) और (p=8)। अज्ञात गुणांक निकालने के लिए दिया पद नियम में रखें।

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Question 72/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_1=17\) और प्रत्येक अगला पद पिछले पद से (9) कम है, तो स्पष्ट नियम क्या होगा?

If \(a_1=17\) and each next term is (9) less than the previous term, what is the explicit rule?

Explanation opens after your attempt

Correct Answer

B. \(a_n=26-9n\)

Step 1

Concept

The first term is (17) and the difference is (-9), so (a_n=17+(n-1)(-9)=26-9n). Treat decrease as a negative difference.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=26-9n\). The first term is (17) and the difference is (-9), so (a_n=17+(n-1)(-9)=26-9n). Treat decrease as a negative difference.

Step 3

Exam Tip

पहला पद (17) और अंतर (-9) है इसलिए (a_n=17+(n-1)(-9)=26-9n)। घटने को ऋणात्मक अंतर मानें।

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Question 73/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(3,9,18,30,\ldots\) को कौन-सा नियम दर्शाता है?

Which rule represents the sequence \(3,9,18,30,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=\frac{3n(n+1)}{2})

Step 1

Concept

This is three times the triangular numbers, so (a_n=\frac{3n(n+1)}{2}). Recognize the pattern from additions (6,9,12).

Step 2

Why this answer is correct

The correct answer is A. (a_n=\frac{3n(n+1)}{2}). This is three times the triangular numbers, so (a_n=\frac{3n(n+1)}{2}). Recognize the pattern from additions (6,9,12).

Step 3

Exam Tip

यह (3) गुना त्रिभुज संख्याओं का क्रम है इसलिए (a_n=\frac{3n(n+1)}{2})। लगातार जोड़ (6,9,12) से पैटर्न पहचानें।

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Question 74/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(12,25,42,63,\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(12,25,42,63,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2n^2+7n+3\)

Step 1

Concept

\(2n^2+7n+3\) gives (12,25,42,63). If second differences are constant, a quadratic rule fits.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^2+7n+3\). \(2n^2+7n+3\) gives (12,25,42,63). If second differences are constant, a quadratic rule fits.

Step 3

Exam Tip

\(2n^2+7n+3\) से (12,25,42,63) मिलते हैं। दूसरे अंतर स्थिर हों तो द्विघात नियम बनता है।

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Question 75/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=\frac{3n}{n+4}\) है तो \(a_n=\frac{9}{7}\) किस पद पर होगा?

If \(a_n=\frac{3n}{n+4}\), at which term will \(a_n=\frac{9}{7}\)?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

From \(\frac{3n}{n+4}=\frac{9}{7}\), (21n=9n+36), so (n=3). None of the given options is correct.

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. From \(\frac{3n}{n+4}=\frac{9}{7}\), (21n=9n+36), so (n=3). None of the given options is correct.

Step 3

Exam Tip

\(\frac{3n}{n+4}=\frac{9}{7}\) से (21n=9n+36) और (n=3) नहीं बल्कि (n=3) मिलता है। दिए विकल्पों में कोई सही नहीं है।

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Question 76/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=4n^2+3\) है तो \(a_3+a_5\) का मान क्या है?

If \(a_n=4n^2+3\), what is the value of \(a_3+a_5\)?

Explanation opens after your attempt

Correct Answer

C. (142)

Step 1

Concept

\(a_3=39\) and \(a_5=103\), so the sum is (142). Find both terms separately before adding.

Step 2

Why this answer is correct

The correct answer is C. (142). \(a_3=39\) and \(a_5=103\), so the sum is (142). Find both terms separately before adding.

Step 3

Exam Tip

\(a_3=39\) और \(a_5=103\), इसलिए योग (142) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें।

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Question 77/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(16,64,144,256,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(16,64,144,256,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_n=16n^2\)

Step 1

Concept

This is \(4^2,8^2,12^2,16^2,\ldots\), so (a_n=(4n)²=16n^-2). In square sequences with equal base gaps, find the base rule.

Step 2

Why this answer is correct

The correct answer is D. \(a_n=16n^2\). This is \(4^2,8^2,12^2,16^2,\ldots\), so (a_n=(4n)²=16n^-2). In square sequences with equal base gaps, find the base rule.

Step 3

Exam Tip

यह \(4^2,8^2,12^2,16^2,\ldots\) है इसलिए (a_n=(4n)²=16n^-2)। सम अंतर वाले वर्गों में आधार का नियम देखें।

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Question 78/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(5,12,23,38,\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(5,12,23,38,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2n^2+n+2\)

Step 1

Concept

\(2n^2+n+2\) gives (5,12,23,38). Increasing differences (7,11,15) indicate a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^2+n+2\). \(2n^2+n+2\) gives (5,12,23,38). Increasing differences (7,11,15) indicate a quadratic rule.

Step 3

Exam Tip

\(2n^2+n+2\) से (5,12,23,38) मिलते हैं। बढ़ते अंतर (7,11,15) द्विघात नियम का संकेत देते हैं।

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Question 79/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=2^n+3n\) है तो पहले चार पद कौन-से होंगे?

If \(a_n=2^n+3n\), what will be the first four terms?

Explanation opens after your attempt

Correct Answer

A. (5,10,17,28)

Step 1

Concept

Putting (n=1,2,3,4) gives (5,10,17,28). Do not forget to add both the power part and the linear part.

Step 2

Why this answer is correct

The correct answer is A. (5,10,17,28). Putting (n=1,2,3,4) gives (5,10,17,28). Do not forget to add both the power part and the linear part.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (5,10,17,28) मिलते हैं। घात और रैखिक भाग दोनों जोड़ना न भूलें।

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Question 80/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(6,-11,16,-21,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(6,-11,16,-21,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(-1)^{n+1}(5n+1))

Step 1

Concept

The magnitude is \(6,11,16,21,\ldots\) and signs start positive and alternate, so (a_n=(-1)^{n+1}(5n+1)). The sign of the first term decides the power.

Step 2

Why this answer is correct

The correct answer is B. (a_n=(-1)^{n+1}(5n+1)). The magnitude is \(6,11,16,21,\ldots\) and signs start positive and alternate, so (a_n=(-1)^{n+1}(5n+1)). The sign of the first term decides the power.

Step 3

Exam Tip

परिमाण \(6,11,16,21,\ldots\) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}(5n+1))। पहले पद का चिह्न शक्ति तय करता है।

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Question 81/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(15,24,33,42,\ldots\) का (40)वाँ पद क्या है?

What is the (40)th term of the sequence \(15,24,33,42,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (366)

Step 1

Concept

The general term is \(a_n=9n+6\), so \(a_{40}=366\). Use the same general rule even for a large term.

Step 2

Why this answer is correct

The correct answer is B. (366). The general term is \(a_n=9n+6\), so \(a_{40}=366\). Use the same general rule even for a large term.

Step 3

Exam Tip

सामान्य पद \(a_n=9n+6\) है इसलिए \(a_{40}=366\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं।

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Question 82/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

एक समानांतर अनुक्रम में \(a_2=19\) और \(a_8=-17\) है। उसका स्पष्ट नियम क्या है?

In an arithmetic sequence, \(a_2=19\) and \(a_8=-17\). What is its explicit rule?

Explanation opens after your attempt

Correct Answer

A. \(a_n=31-6n\)

Step 1

Concept

The change over six gaps is (-36), so (d=-6), hence \(a_n=31-6n\). From two given terms first find the common difference.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=31-6n\). The change over six gaps is (-36), so (d=-6), hence \(a_n=31-6n\). From two given terms first find the common difference.

Step 3

Exam Tip

छह अंतरों में परिवर्तन (-36) है इसलिए (d=-6), अतः \(a_n=31-6n\)। दो दिए पदों से पहले समान अंतर निकालें।

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Question 83/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=n^2+5n\) है तो \(a_n=126\) किस (n) पर होगा?

If \(a_n=n^2+5n\), for which (n) will \(a_n=126\)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

Putting (n=9) gives (81+45=126). Directly checking options is a quick method.

Step 2

Why this answer is correct

The correct answer is B. (9). Putting (n=9) gives (81+45=126). Directly checking options is a quick method.

Step 3

Exam Tip

(n=9) रखने पर (81+45=126) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।

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Question 84/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(4,8,14,22,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(4,8,14,22,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^2+n+2\)

Step 1

Concept

\(n^2+n+2\) gives (4,8,14,22). If second differences are equal, check a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+n+2\). \(n^2+n+2\) gives (4,8,14,22). If second differences are equal, check a quadratic rule.

Step 3

Exam Tip

\(n^2+n+2\) से (4,8,14,22) मिलते हैं। दूसरे अंतर समान हों तो द्विघात नियम देखें।

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Question 85/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=\frac{4n+1}{3n-1}\) है तो \(a_4\) क्या होगा?

If \(a_n=\frac{4n+1}{3n-1}\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{17}{11}\)

Step 1

Concept

(a_4=\frac{4(4)+1}{3(4)-1}=\frac{17}{11}). In a fractional rule substitute (n) in both numerator and denominator.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{17}{11}\). (a_4=\frac{4(4)+1}{3(4)-1}=\frac{17}{11}). In a fractional rule substitute (n) in both numerator and denominator.

Step 3

Exam Tip

(a_4=\frac{4(4)+1}{3(4)-1}=\frac{17}{11})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें।

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Question 86/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(216,343,512,729,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(216,343,512,729,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(n+5)³)

Step 1

Concept

This is \(6^3,7^3,8^3,9^3,\ldots\), so (a_n=(n+5)³). In cube sequences observe the order of base numbers.

Step 2

Why this answer is correct

The correct answer is B. (a_n=(n+5)³). This is \(6^3,7^3,8^3,9^3,\ldots\), so (a_n=(n+5)³). In cube sequences observe the order of base numbers.

Step 3

Exam Tip

यह \(6^3,7^3,8^3,9^3,\ldots\) है इसलिए (a_n=(n+5)³)। घन अनुक्रम में आधार संख्या का क्रम देखें।

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Question 87/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(14,31,54,83,\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(14,31,54,83,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3n^2+8n+3\)

Step 1

Concept

\(3n^2+8n+3\) gives (14,31,54,83). Match options with the initial terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n^2+8n+3\). \(3n^2+8n+3\) gives (14,31,54,83). Match options with the initial terms.

Step 3

Exam Tip

\(3n^2+8n+3\) से (14,31,54,83) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाएं।

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Question 88/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=11-5n\) है तो इस अनुक्रम का समान अंतर क्या है?

If \(a_n=11-5n\), what is the common difference of this sequence?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

In a linear rule the coefficient of (n) is (-5), so the common difference is (-5). Do not miss the sign while reading the coefficient.

Step 2

Why this answer is correct

The correct answer is A. (-5). In a linear rule the coefficient of (n) is (-5), so the common difference is (-5). Do not miss the sign while reading the coefficient.

Step 3

Exam Tip

रैखिक नियम में (n) का गुणांक (-5) है इसलिए समान अंतर (-5) है। गुणांक पढ़ते समय चिह्न न छोड़ें।

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Question 89/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=6n^2-1\) है तो \(a_4+a_2\) का मान क्या होगा?

If \(a_n=6n^2-1\), what is the value of \(a_4+a_2\)?

Explanation opens after your attempt

Correct Answer

B. (120)

Step 1

Concept

\(a_4=95\) and \(a_2=23\), so the sum is (118). The correct option is (118), and both terms should be found separately.

Step 2

Why this answer is correct

The correct answer is B. (120). \(a_4=95\) and \(a_2=23\), so the sum is (118). The correct option is (118), and both terms should be found separately.

Step 3

Exam Tip

\(a_4=95\) और \(a_2=23\), इसलिए योग (118) है। सही विकल्प (118) है और दोनों पद अलग निकालें।

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Question 90/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(70,61,52,43,\ldots\) में (-2) कौन-सा पद है?

In the sequence \(70,61,52,43,\ldots\), which term is (-2)?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

The general term is \(a_n=79-9n\), and (79-9n=-2) gives (n=9). Even in decreasing sequences the position is natural.

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. The general term is \(a_n=79-9n\), and (79-9n=-2) gives (n=9). Even in decreasing sequences the position is natural.

Step 3

Exam Tip

सामान्य पद \(a_n=79-9n\) है और (79-9n=-2) से (n=9)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक होती है।

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Question 91/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=4n^2-3n+8\) है तो पहले तीन पद कौन-से हैं?

If \(a_n=4n^2-3n+8\), what are the first three terms?

Explanation opens after your attempt

Correct Answer

A. (9,18,35)

Step 1

Concept

Putting (n=1,2,3) gives (9,18,35). Calculate each term carefully in a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. (9,18,35). Putting (n=1,2,3) gives (9,18,35). Calculate each term carefully in a quadratic rule.

Step 3

Exam Tip

(n=1,2,3) रखने पर (9,18,35) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें।

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Question 92/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(\frac{6}{5},\frac{9}{8},\frac{14}{13},\frac{21}{20},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{6}{5},\frac{9}{8},\frac{14}{13},\frac{21}{20},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{n^2+5}{n^2+4}\)

Step 1

Concept

The numerator is \(n^2+5\) and the denominator is \(n^2+4\), so \(a_n=\frac{n^2+5}{n^2+4}\). Identify square patterns in fractional sequences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{n^2+5}{n^2+4}\). The numerator is \(n^2+5\) and the denominator is \(n^2+4\), so \(a_n=\frac{n^2+5}{n^2+4}\). Identify square patterns in fractional sequences.

Step 3

Exam Tip

अंश \(n^2+5\) और हर \(n^2+4\) है इसलिए \(a_n=\frac{n^2+5}{n^2+4}\)। भिन्न अनुक्रम में वर्ग पैटर्न पहचानें।

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Question 93/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(\frac{3}{7},\frac{6}{12},\frac{9}{17},\frac{12}{22},\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(\frac{3}{7},\frac{6}{12},\frac{9}{17},\frac{12}{22},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{3n}{5n+2}\)

Step 1

Concept

The numerator is (3n) and the denominator is (5n+2), so \(a_n=\frac{3n}{5n+2}\). Observe the denominator growth carefully.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{3n}{5n+2}\). The numerator is (3n) and the denominator is (5n+2), so \(a_n=\frac{3n}{5n+2}\). Observe the denominator growth carefully.

Step 3

Exam Tip

अंश (3n) और हर (5n+2) है इसलिए \(a_n=\frac{3n}{5n+2}\)। हर की बढ़त को ध्यान से देखें।

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Question 94/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=13n-8\) है तो \(a_9-a_4\) कितना होगा?

If \(a_n=13n-8\), what is \(a_9-a_4\)?

Explanation opens after your attempt

Correct Answer

B. (65)

Step 1

Concept

\(a_9=109\) and \(a_4=44\), so the difference is (65). Calculate both terms separately before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (65). \(a_9=109\) and \(a_4=44\), so the difference is (65). Calculate both terms separately before subtracting.

Step 3

Exam Tip

\(a_9=109\) और \(a_4=44\), इसलिए अंतर (65) है। घटाने से पहले दोनों पदों की अलग गणना करें।

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Question 95/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(7,-14,21,-28,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(7,-14,21,-28,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (a_n=(-1)^{n+1}7n)

Step 1

Concept

The magnitude is (7n) and signs start positive and alternate, so (a_n=(-1)^{n+1}7n). Choose the power of ((-1)) by checking the first term sign.

Step 2

Why this answer is correct

The correct answer is D. (a_n=(-1)^{n+1}7n). The magnitude is (7n) and signs start positive and alternate, so (a_n=(-1)^{n+1}7n). Choose the power of ((-1)) by checking the first term sign.

Step 3

Exam Tip

परिमाण (7n) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}7n)। पहले पद का चिह्न देखकर ((-1)) की शक्ति चुनें।

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Question 96/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(9,22,45,78,\ldots\) के लिए सही नियम कौन-सा है?

Which is the correct rule for the sequence \(9,22,45,78,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5n^2-2n+6\)

Step 1

Concept

\(5n^2-2n+6\) gives (9,22,45,78). The second difference (10) is constant, so a quadratic rule fits.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n^2-2n+6\). \(5n^2-2n+6\) gives (9,22,45,78). The second difference (10) is constant, so a quadratic rule fits.

Step 3

Exam Tip

\(5n^2-2n+6\) से (9,22,45,78) मिलते हैं। दूसरे अंतर (10) स्थिर है इसलिए द्विघात नियम बनेगा।

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Question 97/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=n^2+qn+4\) और \(a_5=54\) है तो (q) का मान क्या है?

If \(a_n=n^2+qn+4\) and \(a_5=54\), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

From (25+5q+4=54), (5q=25) and (q=5). Substitute the given term in the rule to find the unknown constant.

Step 2

Why this answer is correct

The correct answer is C. (5). From (25+5q+4=54), (5q=25) and (q=5). Substitute the given term in the rule to find the unknown constant.

Step 3

Exam Tip

(25+5q+4=54) से (5q=25) और (q=5)। अज्ञात स्थिरांक के लिए दिया पद नियम में रखें।

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Question 98/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

यदि \(a_n=22-4n\) है तो पहला ऋणात्मक पद कौन-सा होगा?

If \(a_n=22-4n\), which will be the first negative term?

Explanation opens after your attempt

Correct Answer

B. (6)वाँ(6)th

Step 1

Concept

\(a_5=2\) and \(a_6=-2\), so the first negative term is the (6)th. Do not count zero or positive terms as negative.

Step 2

Why this answer is correct

The correct answer is B. (6)वाँ / (6)th. \(a_5=2\) and \(a_6=-2\), so the first negative term is the (6)th. Do not count zero or positive terms as negative.

Step 3

Exam Tip

\(a_5=2\) और \(a_6=-2\) है, इसलिए पहला ऋणात्मक पद (6)वाँ है। शून्य या धनात्मक पद को ऋणात्मक न मानें।

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Question 99/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

एक समानांतर अनुक्रम में \(a_5=29\) और \(a_{11}=83\) है। \(a_{15}\) का मान क्या होगा?

In an arithmetic sequence, \(a_5=29\) and \(a_{11}=83\). What is the value of \(a_{15}\)?

Explanation opens after your attempt

Correct Answer

C. (119)

Step 1

Concept

The increase over six gaps is (54), so (d=9), hence (a_{15}=83+4(9)=119). Extend the terms using the common difference.

Step 2

Why this answer is correct

The correct answer is C. (119). The increase over six gaps is (54), so (d=9), hence (a_{15}=83+4(9)=119). Extend the terms using the common difference.

Step 3

Exam Tip

छह अंतरों में वृद्धि (54) है इसलिए (d=9), अतः (a_{15}=83+4(9)=119)। समान अंतर को आगे बढ़ाकर पद निकालें।

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Question 100/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 48

अनुक्रम \(1,15,63,195,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(1,15,63,195,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=n^3+n-1\)

Step 1

Concept

\(n^3+n-1\) does not give the sequence; none of the listed options correctly fits this sequence. Matching options with initial terms is necessary.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^3+n-1\). \(n^3+n-1\) does not give the sequence; none of the listed options correctly fits this sequence. Matching options with initial terms is necessary.

Step 3

Exam Tip

\(n^3+n-1\) से (1,9,29,67) नहीं मिलता; इस क्रम के लिए दिए विकल्पों में सही नियम नहीं है। विकल्पों को शुरुआती पदों से मिलाना जरूरी है।

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Question 101/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=5n^2-3n+2\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=5n^2-3n+2\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (70)

Step 1

Concept

\(a_4=5\times16-12+2=70\). In exams, handle the square part and subtraction separately.

Step 2

Why this answer is correct

The correct answer is C. (70). \(a_4=5\times16-12+2=70\). In exams, handle the square part and subtraction separately.

Step 3

Exam Tip

\(a_4=5\times16-12+2=70\) है। परीक्षा में वर्ग वाला भाग और घटाव अलग-अलग करें।

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Question 102/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(7,24,51,88,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(7,24,51,88,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5n^2+2n\)

Step 1

Concept

Using \(5n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n^2+2n\). Using \(5n^2+2n\) gives the given terms. In exams, substitute (n=1,2,3) to match options.

Step 3

Exam Tip

\(5n^2+2n\) रखने पर दिए पद मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प मिलाएँ।

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Question 103/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=3n^2+4n-5\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=3n^2+4n-5\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (127)

Step 1

Concept

\(a_6=3\times36+24-5=127\). In exams, write positive and negative terms separately.

Step 2

Why this answer is correct

The correct answer is C. (127). \(a_6=3\times36+24-5=127\). In exams, write positive and negative terms separately.

Step 3

Exam Tip

\(a_6=3\times36+24-5=127\) है। परीक्षा में धन और ऋण पदों को अलग लिखें।

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Question 104/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,11,26,47,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,11,26,47,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=3n^2-1\)

Step 1

Concept

\(3n^2-1\) gives (2,11,26,47). In exams, identify a quadratic rule from second differences.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=3n^2-1\). \(3n^2-1\) gives (2,11,26,47). In exams, identify a quadratic rule from second differences.

Step 3

Exam Tip

\(3n^2-1\) से (2,11,26,47) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम पहचानें।

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Question 105/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि (a_n=\frac{n(4n+1)}{2}) है, तो \(a_5\) का मान क्या होगा?

If (a_n=\frac{n(4n+1)}{2}), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{105}{2}\)

Step 1

Concept

\(a_5=\frac{5\times21}{2}=\frac{105}{2}\). In exams, find the bracket value first.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{105}{2}\). \(a_5=\frac{5\times21}{2}=\frac{105}{2}\). In exams, find the bracket value first.

Step 3

Exam Tip

\(a_5=\frac{5\times21}{2}=\frac{105}{2}\) है। परीक्षा में पहले कोष्ठक का मान निकालें।

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Question 106/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(\frac{5}{2},9,\frac{39}{2},34,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(\frac{5}{2},9,\frac{39}{2},34,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=\frac{n(4n+1)}{2})

Step 1

Concept

(\frac{n(4n+1)}{2}) gives the given terms. In exams, test fractional terms with small (n).

Step 2

Why this answer is correct

The correct answer is A. (a_n=\frac{n(4n+1)}{2}). (\frac{n(4n+1)}{2}) gives the given terms. In exams, test fractional terms with small (n).

Step 3

Exam Tip

(\frac{n(4n+1)}{2}) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी छोटे (n) से जाँचें।

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Question 107/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि (a_n=(3n-2)²) है, तो \(a_4\) का मान क्या होगा?

If (a_n=(3n-2)²), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (100)

Step 1

Concept

(a_4=(12-2)²=100). In exams, find the value inside the bracket first.

Step 2

Why this answer is correct

The correct answer is B. (100). (a_4=(12-2)²=100). In exams, find the value inside the bracket first.

Step 3

Exam Tip

(a_4=(12-2)²=100) है। परीक्षा में कोष्ठक का मान पहले निकालें।

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Question 108/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(1,16,49,100,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(1,16,49,100,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=(3n-2)²)

Step 1

Concept

The squares of (3n-2) give (1,16,49,100). In exams, form the base first and then square it.

Step 2

Why this answer is correct

The correct answer is A. (a_n=(3n-2)²). The squares of (3n-2) give (1,16,49,100). In exams, form the base first and then square it.

Step 3

Exam Tip

(3n-2) के वर्ग से (1,16,49,100) मिलते हैं। परीक्षा में पहले आधार बनाकर फिर वर्ग करें।

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Question 109/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=150-11n\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=150-11n\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

B. (73)

Step 1

Concept

\(a_7=150-77=73\). In exams, multiply first in a decreasing formula.

Step 2

Why this answer is correct

The correct answer is B. (73). \(a_7=150-77=73\). In exams, multiply first in a decreasing formula.

Step 3

Exam Tip

\(a_7=150-77=73\) है। परीक्षा में घटते सूत्र में गुणन पहले करें।

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Question 110/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(139,128,117,106,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(139,128,117,106,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=150-11n\)

Step 1

Concept

At (n=1) it gives (139), and at (n=2) it gives (128), so \(a_n=150-11n\). In exams, match the first term of a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=150-11n\). At (n=1) it gives (139), and at (n=2) it gives (128), so \(a_n=150-11n\). In exams, match the first term of a decreasing sequence.

Step 3

Exam Tip

(n=1) पर (139) और (n=2) पर (128) मिलता है, इसलिए \(a_n=150-11n\) है। परीक्षा में घटते अनुक्रम का पहला पद मिलाएँ।

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Question 111/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=8n-5\) है, तो कौन-सा पद (155) के बराबर होगा?

If \(a_n=8n-5\), which term is equal to (155)?

Explanation opens after your attempt

Correct Answer

C. (n=20)

Step 1

Concept

From (8n-5=155), we get (n=20). In exams, equate the formula to the given value to find the term number.

Step 2

Why this answer is correct

The correct answer is C. (n=20). From (8n-5=155), we get (n=20). In exams, equate the formula to the given value to find the term number.

Step 3

Exam Tip

(8n-5=155) से (n=20) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।

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Question 112/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(4,15,26,37,\ldots\) में (125) कौन-सा पद है?

In the sequence \(4,15,26,37,\ldots\), which term is (125)?

Explanation opens after your attempt

Correct Answer

C. बारहवाँ पद(12)th term

Step 1

Concept

Its rule is \(a_n=11n-7\), and (11n-7=125) gives (n=12). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is C. बारहवाँ पद / (12)th term. Its rule is \(a_n=11n-7\), and (11n-7=125) gives (n=12). In exams, equate the given term to the general term.

Step 3

Exam Tip

इसका नियम \(a_n=11n-7\) है और (11n-7=125) से (n=12) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 113/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(3,8,17,32,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(3,8,17,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2^n+n^2\)

Step 1

Concept

\(2^n+n^2\) gives (3,8,17,32). In exams, check combined power-and-square rules.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2^n+n^2\). \(2^n+n^2\) gives (3,8,17,32). In exams, check combined power-and-square rules.

Step 3

Exam Tip

\(2^n+n^2\) से (3,8,17,32) मिलते हैं। परीक्षा में घात और वर्ग वाले संयुक्त नियम जाँचें।

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Question 114/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=3^n+n^2-1\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=3^n+n^2-1\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (35)

Step 1

Concept

\(a_3=27+9-1=35\). In exams, check the power, square, and constant subtraction.

Step 2

Why this answer is correct

The correct answer is B. (35). \(a_3=27+9-1=35\). In exams, check the power, square, and constant subtraction.

Step 3

Exam Tip

\(a_3=27+9-1=35\) है। परीक्षा में घात, वर्ग और स्थिर घटाव तीनों देखें।

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Question 115/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(3,12,35,96,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,12,35,96,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3^n+n^2-1\)

Step 1

Concept

\(3^n+n^2-1\) gives (3,12,35,96). In exams, check a power rule in rapid growth.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3^n+n^2-1\). \(3^n+n^2-1\) gives (3,12,35,96). In exams, check a power rule in rapid growth.

Step 3

Exam Tip

\(3^n+n^2-1\) से (3,12,35,96) मिलते हैं। परीक्षा में तेज वृद्धि में घात वाला नियम जाँचें।

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Question 116/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=7\cdot2^{n-1}+4\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=7\cdot2^{n-1}+4\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (116)

Step 1

Concept

\(a_5=7\cdot2^4+4=116\). In exams, apply the exponent (n-1) carefully.

Step 2

Why this answer is correct

The correct answer is B. (116). \(a_5=7\cdot2^4+4=116\). In exams, apply the exponent (n-1) carefully.

Step 3

Exam Tip

\(a_5=7\cdot2^4+4=116\) है। परीक्षा में (n-1) वाले घातांक को ध्यान से लगाएँ।

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Question 117/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(11,18,32,60,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(11,18,32,60,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=7\cdot2^{n-1}+4\)

Step 1

Concept

\(7\cdot2^{n-1}+4\) gives the given terms. In exams, also check constant addition in geometric forms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=7\cdot2^{n-1}+4\). \(7\cdot2^{n-1}+4\) gives the given terms. In exams, also check constant addition in geometric forms.

Step 3

Exam Tip

\(7\cdot2^{n-1}+4\) से दिए पद मिलते हैं। परीक्षा में गुणोत्तर रूप में स्थिर जोड़ भी जाँचें।

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Question 118/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=4n^2+5n-6\) है, तो \(a_3+a_5\) का मान क्या होगा?

If \(a_n=4n^2+5n-6\), what is the value of \(a_3+a_5\)?

Explanation opens after your attempt

Correct Answer

C. (164)

Step 1

Concept

\(a_3=45\) and \(a_5=119\), so the sum is (164). In exams, find both terms before adding.

Step 2

Why this answer is correct

The correct answer is C. (164). \(a_3=45\) and \(a_5=119\), so the sum is (164). In exams, find both terms before adding.

Step 3

Exam Tip

\(a_3=45\) और \(a_5=119\), इसलिए योग (164) है। परीक्षा में योग से पहले दोनों पद निकालें।

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Question 119/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(3,20,45,78,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,20,45,78,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4n^2+5n-6\)

Step 1

Concept

\(4n^2+5n-6\) gives (3,20,45,78). In exams, choose a quadratic rule when second differences are constant.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n^2+5n-6\). \(4n^2+5n-6\) gives (3,20,45,78). In exams, choose a quadratic rule when second differences are constant.

Step 3

Exam Tip

\(4n^2+5n-6\) से (3,20,45,78) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम चुनें।

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Question 120/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=n^3+3n^2-2\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=n^3+3n^2-2\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

D. (110)

Step 1

Concept

\(a_4=64+48-2=110\). In exams, calculate the cube and square separately.

Step 2

Why this answer is correct

The correct answer is D. (110). \(a_4=64+48-2=110\). In exams, calculate the cube and square separately.

Step 3

Exam Tip

\(a_4=64+48-2=110\) है। परीक्षा में घन और वर्ग दोनों अलग निकालें।

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Question 121/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,18,52,110,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,18,52,110,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^3+3n^2-2\)

Step 1

Concept

\(n^3+3n^2-2\) gives (2,18,52,110). In exams, test cube-based options with small (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^3+3n^2-2\). \(n^3+3n^2-2\) gives (2,18,52,110). In exams, test cube-based options with small (n).

Step 3

Exam Tip

\(n^3+3n^2-2\) से (2,18,52,110) मिलते हैं। परीक्षा में घन आधारित विकल्पों को छोटे (n) से जाँचें।

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Question 122/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=2n^3+n^2+n\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=2n^3+n^2+n\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

\(a_3=54+9+3=66\). In exams, add the cube, square, and linear parts.

Step 2

Why this answer is correct

The correct answer is C. (66). \(a_3=54+9+3=66\). In exams, add the cube, square, and linear parts.

Step 3

Exam Tip

\(a_3=54+9+3=66\) है। परीक्षा में घन, वर्ग और रैखिक भाग जोड़ें।

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Question 123/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(4,22,66,148,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,22,66,148,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2n^3+n^2+n\)

Step 1

Concept

\(2n^3+n^2+n\) gives (4,22,66,148). In exams, also check combined cubic rules.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^3+n^2+n\). \(2n^3+n^2+n\) gives (4,22,66,148). In exams, also check combined cubic rules.

Step 3

Exam Tip

\(2n^3+n^2+n\) से (4,22,66,148) मिलते हैं। परीक्षा में संयुक्त घन नियम भी जाँचें।

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Question 124/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=\frac{3n^2+5n}{4}\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=\frac{3n^2+5n}{4}\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (17)

Step 1

Concept

\(a_4=\frac{48+20}{4}=17\). In exams, simplify the whole numerator and then divide by the denominator.

Step 2

Why this answer is correct

The correct answer is C. (17). \(a_4=\frac{48+20}{4}=17\). In exams, simplify the whole numerator and then divide by the denominator.

Step 3

Exam Tip

\(a_4=\frac{48+20}{4}=17\) है। परीक्षा में अंश पूरा सरल करके हर से भाग दें।

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Question 125/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,\frac{11}{2},\frac{21}{2},17,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(2,\frac{11}{2},\frac{21}{2},17,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=\frac{3n^2+5n}{4}\)

Step 1

Concept

\(\frac{3n^2+5n}{4}\) gives the given terms. In exams, match fractional terms with options too.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{3n^2+5n}{4}\). \(\frac{3n^2+5n}{4}\) gives the given terms. In exams, match fractional terms with options too.

Step 3

Exam Tip

\(\frac{3n^2+5n}{4}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी विकल्पों से मिलाएँ।

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Question 126/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=6n^2-n+4\) है, तो \(a_4:a_2\) क्या होगा?

If \(a_n=6n^2-n+4\), what is \(a_4:a_2\)?

Explanation opens after your attempt

Correct Answer

B. (48:13)

Step 1

Concept

\(a_4=96\) and \(a_2=26\), so the simplified ratio is (48:13). In exams, do not forget to simplify the ratio.

Step 2

Why this answer is correct

The correct answer is B. (48:13). \(a_4=96\) and \(a_2=26\), so the simplified ratio is (48:13). In exams, do not forget to simplify the ratio.

Step 3

Exam Tip

\(a_4=96\) और \(a_2=26\), इसलिए सरल अनुपात (48:13) है। परीक्षा में अनुपात सरल करना न भूलें।

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Question 127/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(9,26,55,96,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(9,26,55,96,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=6n^2-n+4\)

Step 1

Concept

\(6n^2-n+4\) gives (9,26,55,96). In exams, check a quadratic rule when second differences are constant.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=6n^2-n+4\). \(6n^2-n+4\) gives (9,26,55,96). In exams, check a quadratic rule when second differences are constant.

Step 3

Exam Tip

\(6n^2-n+4\) से (9,26,55,96) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम देखें।

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Question 128/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=5^n+n-4\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=5^n+n-4\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (124)

Step 1

Concept

\(a_3=125+3-4=124\). In exams, keep both the power and linear part correct.

Step 2

Why this answer is correct

The correct answer is C. (124). \(a_3=125+3-4=124\). In exams, keep both the power and linear part correct.

Step 3

Exam Tip

\(a_3=125+3-4=124\) है। परीक्षा में घात और रैखिक भाग दोनों सही रखें।

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Question 129/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,23,124,625,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,23,124,625,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5^n+n-4\)

Step 1

Concept

\(5^n+n-4\) gives (2,23,124,625). In exams, also check the small linear part in a power rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5^n+n-4\). \(5^n+n-4\) gives (2,23,124,625). In exams, also check the small linear part in a power rule.

Step 3

Exam Tip

\(5^n+n-4\) से (2,23,124,625) मिलते हैं। परीक्षा में घात वाले नियम में छोटा रैखिक भाग भी जाँचें।

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Question 130/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=13n-10\) है, तो पहले पाँच पदों का औसत क्या होगा?

If \(a_n=13n-10\), what is the average of the first five terms?

Explanation opens after your attempt

Correct Answer

A. (29)

Step 1

Concept

The first five terms are (3,16,29,42,55), and the average is (29). In exams, divide the sum by the number of terms.

Step 2

Why this answer is correct

The correct answer is A. (29). The first five terms are (3,16,29,42,55), and the average is (29). In exams, divide the sum by the number of terms.

Step 3

Exam Tip

पहले पाँच पद (3,16,29,42,55) हैं और औसत (29) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें।

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Question 131/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(3,16,29,42,\ldots\) में (159) कौन-सा पद है?

In the sequence \(3,16,29,42,\ldots\), which term is (159)?

Explanation opens after your attempt

Correct Answer

B. तेरहवाँ पद(13)th term

Step 1

Concept

Its rule is \(a_n=13n-10\), and (13n-10=159) gives (n=13). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is B. तेरहवाँ पद / (13)th term. Its rule is \(a_n=13n-10\), and (13n-10=159) gives (n=13). In exams, equate the given term to the general term.

Step 3

Exam Tip

इसका नियम \(a_n=13n-10\) है और (13n-10=159) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 132/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=n^4-n^2\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=n^4-n^2\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (72)

Step 1

Concept

\(a_3=81-9=72\). In exams, calculate the fourth power and square separately.

Step 2

Why this answer is correct

The correct answer is C. (72). \(a_3=81-9=72\). In exams, calculate the fourth power and square separately.

Step 3

Exam Tip

\(a_3=81-9=72\) है। परीक्षा में चौथी घात और वर्ग अलग-अलग निकालें।

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Question 133/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(0,12,72,240,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(0,12,72,240,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n^4-n^2\)

Step 1

Concept

\(n^4-n^2\) gives (0,12,72,240). In exams, test higher-power options with small (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^4-n^2\). \(n^4-n^2\) gives (0,12,72,240). In exams, test higher-power options with small (n).

Step 3

Exam Tip

\(n^4-n^2\) से (0,12,72,240) मिलते हैं। परीक्षा में उच्च घात वाले विकल्पों को छोटे (n) से जाँचें।

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Question 134/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=4^n+n-3\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=4^n+n-3\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (257)

Step 1

Concept

\(a_4=256+4-3=257\). In exams, add the full linear part after the power.

Step 2

Why this answer is correct

The correct answer is C. (257). \(a_4=256+4-3=257\). In exams, add the full linear part after the power.

Step 3

Exam Tip

\(a_4=256+4-3=257\) है। परीक्षा में घात के बाद पूरा रैखिक भाग जोड़ें।

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Question 135/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,15,64,257,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(2,15,64,257,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4^n+n-3\)

Step 1

Concept

\(4^n+n-3\) gives (2,15,64,257). In exams, check a power rule in rapid growth.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4^n+n-3\). \(4^n+n-3\) gives (2,15,64,257). In exams, check a power rule in rapid growth.

Step 3

Exam Tip

\(4^n+n-3\) से (2,15,64,257) मिलते हैं। परीक्षा में तेज वृद्धि में घात वाला नियम जाँचें।

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Question 136/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=2n^2+9n+1\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=2n^2+9n+1\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (96)

Step 1

Concept

\(a_5=50+45+1=96\). In exams, add both the square and linear parts.

Step 2

Why this answer is correct

The correct answer is C. (96). \(a_5=50+45+1=96\). In exams, add both the square and linear parts.

Step 3

Exam Tip

\(a_5=50+45+1=96\) है। परीक्षा में वर्ग और रैखिक भाग दोनों जोड़ें।

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Question 137/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(12,27,46,69,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(12,27,46,69,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=2n^2+9n+1\)

Step 1

Concept

\(2n^2+9n+1\) gives (12,27,46,69). In exams, test the quadratic rule with the first four terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^2+9n+1\). \(2n^2+9n+1\) gives (12,27,46,69). In exams, test the quadratic rule with the first four terms.

Step 3

Exam Tip

\(2n^2+9n+1\) से (12,27,46,69) मिलते हैं। परीक्षा में वर्गीय नियम को पहले चार पदों से जाँचें।

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Question 138/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=200-12n\) है, तो \(a_9\) का मान क्या होगा?

If \(a_n=200-12n\), what is the value of \(a_9\)?

Explanation opens after your attempt

Correct Answer

D. (92)

Step 1

Concept

\(a_9=200-108=92\). In exams, multiply first in a decreasing formula.

Step 2

Why this answer is correct

The correct answer is D. (92). \(a_9=200-108=92\). In exams, multiply first in a decreasing formula.

Step 3

Exam Tip

\(a_9=200-108=92\) है। परीक्षा में घटते सूत्र में गुणन पहले करें।

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Question 139/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(188,176,164,152,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(188,176,164,152,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=200-12n\)

Step 1

Concept

At (n=1) it gives (188), and at (n=2) it gives (176), so \(a_n=200-12n\). In exams, check the first two terms of a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=200-12n\). At (n=1) it gives (188), and at (n=2) it gives (176), so \(a_n=200-12n\). In exams, check the first two terms of a decreasing sequence.

Step 3

Exam Tip

(n=1) पर (188) और (n=2) पर (176) मिलता है, इसलिए \(a_n=200-12n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।

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Question 140/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=\frac{n(5n-1)}{2}\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=\frac{n(5n-1)}{2}\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

D. (87)

Step 1

Concept

\(a_6=\frac{6\times29}{2}=87\). In exams, find the bracket value first and then divide.

Step 2

Why this answer is correct

The correct answer is D. (87). \(a_6=\frac{6\times29}{2}=87\). In exams, find the bracket value first and then divide.

Step 3

Exam Tip

\(a_6=\frac{6\times29}{2}=87\) है। परीक्षा में पहले कोष्ठक का मान निकालें और फिर भाग दें।

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Question 141/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(2,9,21,38,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,9,21,38,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=\frac{n(5n-1)}{2})

Step 1

Concept

(\frac{n(5n-1)}{2}) gives (2,9,21,38). In exams, also check fractional-form general terms.

Step 2

Why this answer is correct

The correct answer is A. (a_n=\frac{n(5n-1)}{2}). (\frac{n(5n-1)}{2}) gives (2,9,21,38). In exams, also check fractional-form general terms.

Step 3

Exam Tip

(\frac{n(5n-1)}{2}) से (2,9,21,38) मिलते हैं। परीक्षा में भिन्न रूप वाले सामान्य पद भी जाँचें।

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Question 142/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि (a_n=(n+1)³-n) है, तो \(a_4\) का मान क्या होगा?

If (a_n=(n+1)³-n), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (121)

Step 1

Concept

\(a_4=5^3-4=121\). In exams, find the power of the bracket first.

Step 2

Why this answer is correct

The correct answer is C. (121). \(a_4=5^3-4=121\). In exams, find the power of the bracket first.

Step 3

Exam Tip

\(a_4=5^3-4=121\) है। परीक्षा में पहले कोष्ठक की घात निकालें।

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Question 143/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(7,25,61,121,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(7,25,61,121,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=(n+1)³-n)

Step 1

Concept

((n+1)³-n) gives (7,25,61,121). In exams, check shifted cube rules.

Step 2

Why this answer is correct

The correct answer is A. (a_n=(n+1)³-n). ((n+1)³-n) gives (7,25,61,121). In exams, check shifted cube rules.

Step 3

Exam Tip

((n+1)³-n) से (7,25,61,121) मिलते हैं। परीक्षा में स्थानांतरित घन नियमों को जाँचें।

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Question 144/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=3\cdot2^n+2n^2\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=3\cdot2^n+2n^2\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (80)

Step 1

Concept

\(a_4=3\cdot16+2\times16=80\). In exams, add both the power and square parts.

Step 2

Why this answer is correct

The correct answer is C. (80). \(a_4=3\cdot16+2\times16=80\). In exams, add both the power and square parts.

Step 3

Exam Tip

\(a_4=3\cdot16+2\times16=80\) है। परीक्षा में घात और वर्ग दोनों जोड़ें।

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Question 145/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(8,20,42,80,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(8,20,42,80,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3\cdot2^n+2n^2\)

Step 1

Concept

\(3\cdot2^n+2n^2\) gives the given terms. In exams, match combined power-and-square rules.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3\cdot2^n+2n^2\). \(3\cdot2^n+2n^2\) gives the given terms. In exams, match combined power-and-square rules.

Step 3

Exam Tip

\(3\cdot2^n+2n^2\) से दिए पद मिलते हैं। परीक्षा में घात और वर्ग वाले संयुक्त नियम मिलाएँ।

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Question 146/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=7n^2-4n+1\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=7n^2-4n+1\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

D. (156)

Step 1

Concept

\(a_5=175-20+1=156\). In exams, subtract the linear part from the quadratic part.

Step 2

Why this answer is correct

The correct answer is D. (156). \(a_5=175-20+1=156\). In exams, subtract the linear part from the quadratic part.

Step 3

Exam Tip

\(a_5=175-20+1=156\) है। परीक्षा में वर्गीय भाग से रैखिक भाग घटाएँ।

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Question 147/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(4,21,52,97,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,21,52,97,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=7n^2-4n+1\)

Step 1

Concept

\(7n^2-4n+1\) gives (4,21,52,97). In exams, identify a quadratic rule by equal second differences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=7n^2-4n+1\). \(7n^2-4n+1\) gives (4,21,52,97). In exams, identify a quadratic rule by equal second differences.

Step 3

Exam Tip

\(7n^2-4n+1\) से (4,21,52,97) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम पहचानें।

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Question 148/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(8,27,56,95,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(8,27,56,95,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_n=5n^2+4n-1\)

Step 1

Concept

\(5n^2+4n-1\) gives (8,27,56,95). In exams, test the rule on the first four terms.

Step 2

Why this answer is correct

The correct answer is D. \(a_n=5n^2+4n-1\). \(5n^2+4n-1\) gives (8,27,56,95). In exams, test the rule on the first four terms.

Step 3

Exam Tip

\(5n^2+4n-1\) से (8,27,56,95) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।

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Question 149/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

यदि \(a_n=\frac{n(3n+5)}{2}\) है, तो \(a_8\) का मान क्या होगा?

If \(a_n=\frac{n(3n+5)}{2}\), what is the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

C. (116)

Step 1

Concept

\(a_8=\frac{8\times29}{2}=116\). In exams, find the bracket value first and simplify.

Step 2

Why this answer is correct

The correct answer is C. (116). \(a_8=\frac{8\times29}{2}=116\). In exams, find the bracket value first and simplify.

Step 3

Exam Tip

\(a_8=\frac{8\times29}{2}=116\) है। परीक्षा में पहले कोष्ठक का मान निकालकर सरल करें।

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Question 150/150 Expert Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 49

अनुक्रम \(3,14,59,266,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(3,14,59,266,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=2\cdot5^{n-1}+n^2\)

Step 1

Concept

\(2\cdot5^{n-1}+n^2\) gives the given terms. In exams, check both the power and square in rapid growth.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=2\cdot5^{n-1}+n^2\). \(2\cdot5^{n-1}+n^2\) gives the given terms. In exams, check both the power and square in rapid growth.

Step 3

Exam Tip

\(2\cdot5^{n-1}+n^2\) से दिए पद मिलते हैं। परीक्षा में तेज वृद्धि में घात और वर्ग दोनों जाँचें।

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Class 9 Mathematics - Sequences and Progressions - Explicit or general rule Expert Quiz

अनुक्रम \(3,10,21,36,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n^2-2n+5\) है, तो \(a_6\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(5,16,33,56,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=4n^2+n-7\) है, तो \(a_5-a_2\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(2,9,22,41,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (a_n=\frac{n(n+3)}{2}+2) है, तो \(a_7\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(4,9,16,25,\ldots\) के लिए कौन-सा सामान्य पद सही है?

Concept

Why this answer is correct

Exam Tip

यदि (a_n=(2n-1)2) है, तो \(a_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=2n^2+5n-3\) है, तो \(a_4+a_2\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(4,15,34,61,\ldots\) का सामान्य पद क्या है?

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यदि \(a_n=7n-4\) है, तो \(a_{15}\) का मान क्या होगा?

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अनुक्रम \(120,112,104,96,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

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यदि \(a_n=9n+2\) है, तो कौन-सा पद (146) के बराबर होगा?

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अनुक्रम \(6,15,24,33,\ldots\) में (150) कौन-सा पद है?

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अनुक्रम \(2,5,10,17,\ldots\) का सामान्य पद क्या है?

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यदि \(a_n=n^2+1\) है, तो कौन-सा पद (101) के बराबर होगा?

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यदि \(a_n=2^n+3n\) है, तो \(a_5\) का मान क्या होगा?

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अनुक्रम \(5,10,17,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

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यदि \(a_n=3^n-2n+1\) है, तो \(a_4\) का मान क्या होगा?

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अनुक्रम \(2,6,22,74,\ldots\) का सामान्य पद क्या है?

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यदि (a_n=(2n-1)²) है, तो \(a_5\) का मान क्या होगा?