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

Question 1/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(3,6,9,12,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,6,9,12,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=3n\)

Step 1

Concept

Each term is a multiple of (3), so \(a_n=3n\). In exams, match the first few terms with (n).

Step 2

Why this answer is correct

The correct answer is C. \(a_n=3n\). Each term is a multiple of (3), so \(a_n=3n\). In exams, match the first few terms with (n).

Step 3

Exam Tip

हर पद (3) का गुणज है, इसलिए \(a_n=3n\) है। परीक्षा में पहले कुछ पदों को (n) से मिलाकर देखें।

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Question 2/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(5,10,15,20,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,10,15,20,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5n\)

Step 1

Concept

This is the sequence of multiples of (5). In exams, quickly check \(a_n=dn\) for multiple-based sequences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n\). This is the sequence of multiples of (5). In exams, quickly check \(a_n=dn\) for multiple-based sequences.

Step 3

Exam Tip

यह (5) के पहाड़े का अनुक्रम है। परीक्षा में गुणज वाले अनुक्रमों में \(a_n=dn\) तुरंत जाँचें।

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Question 3/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(2,4,6,8,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,4,6,8,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=2n\)

Step 1

Concept

This is the sequence of even numbers, so \(a_n=2n\). In exams, remember (2n) for even numbers.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=2n\). This is the sequence of even numbers, so \(a_n=2n\). In exams, remember (2n) for even numbers.

Step 3

Exam Tip

यह सम संख्याओं का अनुक्रम है, इसलिए \(a_n=2n\) है। परीक्षा में सम संख्याओं के लिए (2n) याद रखें।

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Question 4/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(1,3,5,7,\ldots\) का स्पष्ट नियम कौन-सा है?

Which explicit rule represents the sequence \(1,3,5,7,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=2n-1\)

Step 1

Concept

This is the sequence of odd numbers, so \(a_n=2n-1\). In exams, check the rule by putting (n=1).

Step 2

Why this answer is correct

The correct answer is C. \(a_n=2n-1\). This is the sequence of odd numbers, so \(a_n=2n-1\). In exams, check the rule by putting (n=1).

Step 3

Exam Tip

यह विषम संख्याओं का अनुक्रम है, इसलिए \(a_n=2n-1\) है। परीक्षा में पहले पद के लिए (n=1) रखकर नियम जाँचें।

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Question 5/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=n^2\) है, तो अनुक्रम के पहले तीन पद क्या होंगे?

If \(a_n=n^2\), what are the first three terms of the sequence?

Explanation opens after your attempt

Correct Answer

B. (1,4,9)

Step 1

Concept

Putting (n=1,2,3) gives (1,4,9). In exams, use small values of (n) for first terms.

Step 2

Why this answer is correct

The correct answer is B. (1,4,9). Putting (n=1,2,3) gives (1,4,9). In exams, use small values of (n) for first terms.

Step 3

Exam Tip

(n=1,2,3) रखने पर (1,4,9) मिलते हैं। परीक्षा में पहले पदों के लिए (n) के छोटे मान रखें।

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Question 6/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(4,7,10,13,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,7,10,13,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=3n+1\)

Step 1

Concept

The first term is (4) and the difference is (3), so \(a_n=3n+1\). In exams, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n+1\). The first term is (4) and the difference is (3), so \(a_n=3n+1\). In exams, use (a_n=a+(n-1)d).

Step 3

Exam Tip

पहला पद (4) और अंतर (3) है, इसलिए \(a_n=3n+1\) है। परीक्षा में (a_n=a+(n-1)d) का प्रयोग करें।

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Question 7/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

B. (22)

Step 1

Concept

\(a_6=4\times6-2=22\). In exams, multiply first and subtract afterward.

Step 2

Why this answer is correct

The correct answer is B. (22). \(a_6=4\times6-2=22\). In exams, multiply first and subtract afterward.

Step 3

Exam Tip

\(a_6=4\times6-2=22\) है। परीक्षा में गुणा पहले और घटाव बाद में करें।

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Question 8/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(10,20,30,40,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(10,20,30,40,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=10n\)

Step 1

Concept

Each term is a multiple of (10), so \(a_n=10n\). In exams, write the rule by observing the common difference of multiples.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=10n\). Each term is a multiple of (10), so \(a_n=10n\). In exams, write the rule by observing the common difference of multiples.

Step 3

Exam Tip

हर पद (10) का गुणज है, इसलिए \(a_n=10n\) है। परीक्षा में गुणजों का अंतर देखकर नियम लिखें।

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

यदि \(a_n=7n\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=7n\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

D. (28)

Step 1

Concept

\(a_4=7\times4=28\). In exams, replace (n) with the term number.

Step 2

Why this answer is correct

The correct answer is D. (28). \(a_4=7\times4=28\). In exams, replace (n) with the term number.

Step 3

Exam Tip

\(a_4=7\times4=28\) है। परीक्षा में (n) की जगह पद संख्या रखें।

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Question 10/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

Which general term is correct for the sequence \(6,11,16,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5n+1\)

Step 1

Concept

The first term is (6) and the difference is (5), so \(a_n=5n+1\). In exams, check the formula on the first two terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n+1\). The first term is (6) and the difference is (5), so \(a_n=5n+1\). In exams, check the formula on the first two terms.

Step 3

Exam Tip

पहला पद (6) और अंतर (5) है, इसलिए \(a_n=5n+1\) है। परीक्षा में सूत्र को पहले दो पदों पर जाँचें।

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Question 11/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=n+9\) है, तो अनुक्रम का पहला पद क्या है?

If \(a_n=n+9\), what is the first term of the sequence?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

For the first term, putting (n=1) gives \(a_1=10\). In exams, always put (n=1) for the first term.

Step 2

Why this answer is correct

The correct answer is B. (10). For the first term, putting (n=1) gives \(a_1=10\). In exams, always put (n=1) for the first term.

Step 3

Exam Tip

पहले पद के लिए (n=1) रखने पर \(a_1=10\) मिलता है। परीक्षा में पहले पद के लिए हमेशा (n=1) रखें।

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Question 12/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(9,18,27,36,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(9,18,27,36,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=9n\)

Step 1

Concept

This is the sequence of multiples of (9). In exams, write (kn) for the (n)th multiple.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=9n\). This is the sequence of multiples of (9). In exams, write (kn) for the (n)th multiple.

Step 3

Exam Tip

यह (9) के गुणजों का अनुक्रम है। परीक्षा में (n)वें गुणज के लिए (kn) लिखें।

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Question 13/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

D. (11)

Step 1

Concept

\(a_3=3\times3+2=11\). In exams, put the term number directly into the formula.

Step 2

Why this answer is correct

The correct answer is D. (11). \(a_3=3\times3+2=11\). In exams, put the term number directly into the formula.

Step 3

Exam Tip

\(a_3=3\times3+2=11\) है। परीक्षा में पद संख्या को सीधे सूत्र में रखें।

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Question 14/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(7,14,21,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(7,14,21,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=7n\)

Step 1

Concept

Each term is obtained by multiplying by (7), so \(a_n=7n\). In exams, identify table-based sequences quickly.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=7n\). Each term is obtained by multiplying by (7), so \(a_n=7n\). In exams, identify table-based sequences quickly.

Step 3

Exam Tip

हर पद (7) से गुणा करके मिलता है, इसलिए \(a_n=7n\) है। परीक्षा में पहाड़े वाले अनुक्रम जल्दी पहचानें।

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Question 15/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=2n+5\) है, तो \(a_1\) और \(a_2\) क्या होंगे?

If \(a_n=2n+5\), what are \(a_1\) and \(a_2\)?

Explanation opens after your attempt

Correct Answer

A. (7,9)

Step 1

Concept

Putting (n=1) and (n=2) gives (7) and (9). In exams, find the first two terms to check the rule.

Step 2

Why this answer is correct

The correct answer is A. (7,9). Putting (n=1) and (n=2) gives (7) and (9). In exams, find the first two terms to check the rule.

Step 3

Exam Tip

(n=1) और (n=2) रखने पर (7) और (9) मिलते हैं। परीक्षा में पहले दो पद निकालकर नियम की जाँच करें।

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Question 16/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(12,15,18,21,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(12,15,18,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=3n+9\)

Step 1

Concept

The first term is (12) and the difference is (3), so \(a_n=3n+9\). In exams, simplify (a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. \(a_n=3n+9\). The first term is (12) and the difference is (3), so \(a_n=3n+9\). In exams, simplify (a+(n-1)d).

Step 3

Exam Tip

पहला पद (12) और अंतर (3) है, इसलिए \(a_n=3n+9\) है। परीक्षा में (a+(n-1)d) को सरल करें।

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Question 17/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=6n-1\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=6n-1\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (29)

Step 1

Concept

\(a_5=6\times5-1=29\). In exams, do not forget the final subtraction.

Step 2

Why this answer is correct

The correct answer is C. (29). \(a_5=6\times5-1=29\). In exams, do not forget the final subtraction.

Step 3

Exam Tip

\(a_5=6\times5-1=29\) है। परीक्षा में अंतिम घटाव को भूलें नहीं।

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Question 18/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(1,4,9,16,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(1,4,9,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=n^2\)

Step 1

Concept

These are perfect squares, so \(a_n=n^2\). In exams, recognize (1,4,9,16) as square numbers.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=n^2\). These are perfect squares, so \(a_n=n^2\). In exams, recognize (1,4,9,16) as square numbers.

Step 3

Exam Tip

ये पूर्ण वर्ग हैं, इसलिए \(a_n=n^2\) है। परीक्षा में (1,4,9,16) को वर्ग संख्याओं के रूप में पहचानें।

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Question 19/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

C. (17)

Step 1

Concept

\(a_4=4^2+1=17\). In exams, find the square and then add (1).

Step 2

Why this answer is correct

The correct answer is C. (17). \(a_4=4^2+1=17\). In exams, find the square and then add (1).

Step 3

Exam Tip

\(a_4=4^2+1=17\) है। परीक्षा में वर्ग निकालकर (1) जोड़ें।

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Question 20/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(2,5,10,17,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,5,10,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The terms are obtained from \(n^2+1\). In exams, check options by putting (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+1\). The terms are obtained from \(n^2+1\). In exams, check options by putting (n=1,2,3).

Step 3

Exam Tip

ये पद \(n^2+1\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प जाँचें।

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Question 21/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(9,8,7,6,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(9,8,7,6,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=10-n\)

Step 1

Concept

\(At (n=1), it gives (9), and at (n=2), it gives (8). In exams, for a decreasing difference of (1), think (a_n=\)constant-n).

Step 2

Why this answer is correct

\(The correct answer is A. (a_n=10-n). At (n=1), it gives (9), and at (n=2), it gives (8). In exams, for a decreasing difference of (1), think (a_n=\)constant-n).

Step 3

Exam Tip

(n=1) पर (9) और (n=2) पर (8) मिलता है। \(परीक्षा में घटते हुए (1) के अंतर पर (a_n=\)स्थिर-n) सोचें।

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Question 22/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=15-2n\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=15-2n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

\(a_5=15-10=5\). In exams, calculate (2n) first.

Step 2

Why this answer is correct

The correct answer is B. (5). \(a_5=15-10=5\). In exams, calculate (2n) first.

Step 3

Exam Tip

\(a_5=15-10=5\) है। परीक्षा में पहले (2n) का मान निकालें।

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Question 23/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(13,11,9,7,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(13,11,9,7,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=15-2n\)

Step 1

Concept

The first term is (13) and the difference is (-2), so \(a_n=15-2n\). In exams, treat a decreasing difference as negative.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=15-2n\). The first term is (13) and the difference is (-2), so \(a_n=15-2n\). In exams, treat a decreasing difference as negative.

Step 3

Exam Tip

पहला पद (13) है और अंतर (-2) है, इसलिए \(a_n=15-2n\) है। परीक्षा में घटते अंतर को ऋणात्मक मानें।

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Question 24/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

\(a_3=2^3=8\). In exams, replace the exponent by the term number in power formulas.

Step 2

Why this answer is correct

The correct answer is C. (8). \(a_3=2^3=8\). In exams, replace the exponent by the term number in power formulas.

Step 3

Exam Tip

\(a_3=2^3=8\) है। परीक्षा में घात वाले सूत्र में घातांक को पद संख्या से बदलें।

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Question 25/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(2,4,8,16,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,4,8,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=2^n\)

Step 1

Concept

Each term is a power of (2), so \(a_n=2^n\). In exams, recognize geometric-type growth using powers.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=2^n\). Each term is a power of (2), so \(a_n=2^n\). In exams, recognize geometric-type growth using powers.

Step 3

Exam Tip

प्रत्येक पद (2) की घात है, इसलिए \(a_n=2^n\) है। परीक्षा में गुणोत्तर जैसी वृद्धि को घात से पहचानें।

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Question 26/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=3^n\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=3^n\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

\(a_2=3^2=9\). In exams, identify the base and exponent separately.

Step 2

Why this answer is correct

The correct answer is C. (9). \(a_2=3^2=9\). In exams, identify the base and exponent separately.

Step 3

Exam Tip

\(a_2=3^2=9\) है। परीक्षा में आधार और घातांक को अलग पहचानें।

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Question 27/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(3,9,27,81,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(3,9,27,81,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=3^n\)

Step 1

Concept

These terms are consecutive powers of (3). In exams, check \(3^n\) when you see (3,9,27).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=3^n\). These terms are consecutive powers of (3). In exams, check \(3^n\) when you see (3,9,27).

Step 3

Exam Tip

ये पद (3) की क्रमिक घातें हैं। परीक्षा में (3,9,27) देखकर \(3^n\) जाँचें।

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Question 28/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(a_5=25-5=20\). In exams, find the square first and then subtract (n).

Step 2

Why this answer is correct

The correct answer is C. (20). \(a_5=25-5=20\). In exams, find the square first and then subtract (n).

Step 3

Exam Tip

\(a_5=25-5=20\) है। परीक्षा में पहले वर्ग निकालें और फिर (n) घटाएँ।

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Question 29/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(0,2,6,12,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(0,2,6,12,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(n^2-n\) gives (0,2,6,12). In exams, substitute (n=1,2,3) in the options to match.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2-n\). Using \(n^2-n\) gives (0,2,6,12). In exams, substitute (n=1,2,3) in the options to match.

Step 3

Exam Tip

\(n^2-n\) रखने पर (0,2,6,12) मिलते हैं। परीक्षा में विकल्पों में (n=1,2,3) रखकर मिलान करें।

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Question 30/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=4n+3\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=4n+3\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

\(a_2=4\times2+3=11\). In exams, put (2) in place of (n) and simplify.

Step 2

Why this answer is correct

The correct answer is B. (11). \(a_2=4\times2+3=11\). In exams, put (2) in place of (n) and simplify.

Step 3

Exam Tip

\(a_2=4\times2+3=11\) है। परीक्षा में (n) की जगह (2) रखकर सरल करें।

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Question 31/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(7,11,15,19,\ldots\) के लिए सही नियम कौन-सा है?

Which rule is correct for the sequence \(7,11,15,19,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, take the common difference as the coefficient of (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n+3\). The first term is (7) and the difference is (4), so \(a_n=4n+3\). In exams, take the common difference as the coefficient of (n).

Step 3

Exam Tip

पहला पद (7) और अंतर (4) है, इसलिए \(a_n=4n+3\) है। परीक्षा में अंतर को (n) का गुणांक मानें।

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Question 32/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=8n-3\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=8n-3\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (29)

Step 1

Concept

\(a_4=8\times4-3=29\). In exams, subtract (3) only after multiplying.

Step 2

Why this answer is correct

The correct answer is B. (29). \(a_4=8\times4-3=29\). In exams, subtract (3) only after multiplying.

Step 3

Exam Tip

\(a_4=8\times4-3=29\) है। परीक्षा में गुणा के बाद ही (3) घटाएँ।

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Question 33/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(5,13,21,29,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(5,13,21,29,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=8n-3\)

Step 1

Concept

The difference is (8), and at (n=1) the value must be (5), so \(a_n=8n-3\). In exams, find the constant using the first term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=8n-3\). The difference is (8), and at (n=1) the value must be (5), so \(a_n=8n-3\). In exams, find the constant using the first term.

Step 3

Exam Tip

अंतर (8) है और (n=1) पर (5) चाहिए, इसलिए \(a_n=8n-3\) है। परीक्षा में पहले पद से स्थिर संख्या निकालें।

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Question 34/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

\(a_6=\frac{6}{2}=3\). In exams, substitute (n) first in fractional formulas.

Step 2

Why this answer is correct

The correct answer is B. (3). \(a_6=\frac{6}{2}=3\). In exams, substitute (n) first in fractional formulas.

Step 3

Exam Tip

\(a_6=\frac{6}{2}=3\) है। परीक्षा में भिन्न वाले सूत्र में पहले (n) रखें।

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Question 35/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(\frac{1}{2},1,\frac{3}{2},2,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=\frac{n}{2}\)

Step 1

Concept

Each term is half of (n). In exams, match fractional sequences using small values of (n).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=\frac{n}{2}\). Each term is half of (n). In exams, match fractional sequences using small values of (n).

Step 3

Exam Tip

हर पद (n) का आधा है। परीक्षा में भिन्न अनुक्रम को छोटे (n) मानों से मिलाएँ।

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Question 36/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(2,8,18,32,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,8,18,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=2n^2\)

Step 1

Concept

These terms come from \(2n^2\). In exams, test the square-based option on the first three terms.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=2n^2\). These terms come from \(2n^2\). In exams, test the square-based option on the first three terms.

Step 3

Exam Tip

ये पद \(2n^2\) से मिलते हैं। परीक्षा में वर्ग वाले विकल्प को पहले तीन पदों पर जाँचें।

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Question 37/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=3n-2\) है, तो कौन-सा पद (13) के बराबर होगा?

If \(a_n=3n-2\), which term will be equal to (13)?

Explanation opens after your attempt

Correct Answer

C. (n=5)

Step 1

Concept

From (3n-2=13), we get (n=5). In exams, when term number is asked, equate the formula to the given value.

Step 2

Why this answer is correct

The correct answer is C. (n=5). From (3n-2=13), we get (n=5). In exams, when term number is asked, equate the formula to the given value.

Step 3

Exam Tip

(3n-2=13) से (n=5) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।

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Question 38/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(1,4,7,10,\ldots\) में (16) कौन-सा पद है?

In the sequence \(1,4,7,10,\ldots\), which term is (16)?

Explanation opens after your attempt

Correct Answer

C. छठा पद(6)th term

Step 1

Concept

Its rule is \(a_n=3n-2\), and (3n-2=16) gives (n=6). In exams, form the general term first to find the term number.

Step 2

Why this answer is correct

The correct answer is C. छठा पद / (6)th term. Its rule is \(a_n=3n-2\), and (3n-2=16) gives (n=6). In exams, form the general term first to find the term number.

Step 3

Exam Tip

इसका नियम \(a_n=3n-2\) है और (3n-2=16) से (n=6) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।

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Question 39/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=n+4\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=n+4\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

\(a_7=7+4=11\). In exams, substitute directly in simple linear formulas.

Step 2

Why this answer is correct

The correct answer is C. (11). \(a_7=7+4=11\). In exams, substitute directly in simple linear formulas.

Step 3

Exam Tip

\(a_7=7+4=11\) है। परीक्षा में सरल रैखिक सूत्रों में सीधे प्रतिस्थापन करें।

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Question 40/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(5,6,7,8,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(5,6,7,8,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=n+4\)

Step 1

Concept

When (n=1), the value should be (5), so \(a_n=n+4\). In exams, relate (n) to the first term in consecutive-number sequences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n+4\). When (n=1), the value should be (5), so \(a_n=n+4\). In exams, relate (n) to the first term in consecutive-number sequences.

Step 3

Exam Tip

जब (n=1), तब मान (5) चाहिए, इसलिए \(a_n=n+4\) है। परीक्षा में लगातार संख्याओं में पहले पद से (n) का संबंध देखें।

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Question 41/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=12n\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=12n\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

\(a_3=12\times3=36\). In exams, use the multiplication table.

Step 2

Why this answer is correct

The correct answer is C. (36). \(a_3=12\times3=36\). In exams, use the multiplication table.

Step 3

Exam Tip

\(a_3=12\times3=36\) है। परीक्षा में गुणा तालिका का उपयोग करें।

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Question 42/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(12,24,36,48,\ldots\) का स्पष्ट नियम क्या है?

What is the explicit rule of the sequence \(12,24,36,48,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=12n\)

Step 1

Concept

Every term is a multiple of (12). In exams, write equal multiples as \(a_n=kn\).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=12n\). Every term is a multiple of (12). In exams, write equal multiples as \(a_n=kn\).

Step 3

Exam Tip

हर पद (12) का गुणज है। परीक्षा में समान गुणजों को \(a_n=kn\) से लिखें।

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Question 43/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=5n+4\) है, तो \(a_1\) का मान क्या होगा?

If \(a_n=5n+4\), what is the value of \(a_1\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

\(a_1=5\times1+4=9\). In exams, put (n=1) for the first term.

Step 2

Why this answer is correct

The correct answer is C. (9). \(a_1=5\times1+4=9\). In exams, put (n=1) for the first term.

Step 3

Exam Tip

\(a_1=5\times1+4=9\) है। परीक्षा में पहले पद के लिए (n=1) रखें।

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Question 44/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(9,14,19,24,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(9,14,19,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=5n+4\)

Step 1

Concept

The first term is (9) and the difference is (5), so \(a_n=5n+4\). In exams, find the constant part from the first term.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n+4\). The first term is (9) and the difference is (5), so \(a_n=5n+4\). In exams, find the constant part from the first term.

Step 3

Exam Tip

पहला पद (9) और अंतर (5) है, इसलिए \(a_n=5n+4\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।

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Question 45/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि (a_n=\frac{n(n+1)}{2}) है, तो \(a_4\) का मान क्या होगा?

If (a_n=\frac{n(n+1)}{2}), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(a_4=\frac{4\times5}{2}=10\). In exams, first find (n(n+1)) and then divide by (2).

Step 2

Why this answer is correct

The correct answer is B. (10). \(a_4=\frac{4\times5}{2}=10\). In exams, first find (n(n+1)) and then divide by (2).

Step 3

Exam Tip

\(a_4=\frac{4\times5}{2}=10\) है। परीक्षा में पहले (n(n+1)) निकालें और फिर (2) से भाग दें।

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Question 46/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(1,3,6,10,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(1,3,6,10,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

This is the sequence of triangular numbers. In exams, check (\frac{n(n+1)}{2}) when you see (1,3,6,10).

Step 2

Why this answer is correct

The correct answer is C. (a_n=\frac{n(n+1)}{2}). This is the sequence of triangular numbers. In exams, check (\frac{n(n+1)}{2}) when you see (1,3,6,10).

Step 3

Exam Tip

यह त्रिभुज संख्याओं का अनुक्रम है। परीक्षा में (1,3,6,10) देखकर (\frac{n(n+1)}{2}) जाँचें।

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

यदि \(a_n=100-5n\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=100-5n\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (70)

Step 1

Concept

\(a_6=100-30=70\). In exams, subtract (5n) correctly.

Step 2

Why this answer is correct

The correct answer is C. (70). \(a_6=100-30=70\). In exams, subtract (5n) correctly.

Step 3

Exam Tip

\(a_6=100-30=70\) है। परीक्षा में (5n) को सही घटाएँ।

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Question 48/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(4,16,36,64,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,16,36,64,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=4n^2\)

Step 1

Concept

These terms are (4) times square numbers, so \(a_n=4n^2\). In exams, substitute (n=1,2,3) to match.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=4n^2\). These terms are (4) times square numbers, so \(a_n=4n^2\). In exams, substitute (n=1,2,3) to match.

Step 3

Exam Tip

ये पद (4) गुना वर्ग संख्याएँ हैं, इसलिए \(a_n=4n^2\) है। परीक्षा में (n=1,2,3) रखकर मिलान करें।

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Question 49/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

\(a_4=2^4-1=15\). In exams, find the power first and then subtract (1).

Step 2

Why this answer is correct

The correct answer is C. (15). \(a_4=2^4-1=15\). In exams, find the power first and then subtract (1).

Step 3

Exam Tip

\(a_4=2^4-1=15\) है। परीक्षा में पहले घात निकालें और फिर (1) घटाएँ।

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

अनुक्रम \(20,17,14,11,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(20,17,14,11,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=23-3n\)

Step 1

Concept

The first term is (20) and the difference is (-3), so \(a_n=23-3n\). In exams, treat the common difference as negative in decreasing sequences.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=23-3n\). The first term is (20) and the difference is (-3), so \(a_n=23-3n\). In exams, treat the common difference as negative in decreasing sequences.

Step 3

Exam Tip

पहला पद (20) और अंतर (-3) है, इसलिए \(a_n=23-3n\) है। परीक्षा में घटते अनुक्रम में अंतर को ऋणात्मक मानें।

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

अनुक्रम \(4,8,12,16,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,8,12,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4n\)

Step 1

Concept

Each term is a multiple of (4), so \(a_n=4n\). In exams, check multiple-based sequences using (kn).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n\). Each term is a multiple of (4), so \(a_n=4n\). In exams, check multiple-based sequences using (kn).

Step 3

Exam Tip

हर पद (4) का गुणज है, इसलिए \(a_n=4n\) है। परीक्षा में गुणज वाले अनुक्रमों को (kn) से जाँचें।

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Question 52/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=6n+2\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=6n+2\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

\(a_3=6\times3+2=20\). In exams, multiply first and then add the constant.

Step 2

Why this answer is correct

The correct answer is B. (20). \(a_3=6\times3+2=20\). In exams, multiply first and then add the constant.

Step 3

Exam Tip

\(a_3=6\times3+2=20\) है। परीक्षा में पहले गुणा करें और फिर स्थिर संख्या जोड़ें।

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Question 53/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(11,22,33,44,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(11,22,33,44,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=11n\)

Step 1

Concept

Each term is a multiple of (11), so \(a_n=11n\) is correct. In exams, identify equal multiples directly.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=11n\). Each term is a multiple of (11), so \(a_n=11n\) is correct. In exams, identify equal multiples directly.

Step 3

Exam Tip

हर पद (11) का गुणज है, इसलिए \(a_n=11n\) सही है। परीक्षा में समान गुणजों को सीधे पहचानें।

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Question 54/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=9n-4\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=9n-4\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (32)

Step 1

Concept

\(a_4=9\times4-4=32\). In exams, subtract only after multiplying.

Step 2

Why this answer is correct

The correct answer is C. (32). \(a_4=9\times4-4=32\). In exams, subtract only after multiplying.

Step 3

Exam Tip

\(a_4=9\times4-4=32\) है। परीक्षा में गुणा के बाद घटाव करें।

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Question 55/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(3,8,13,18,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,8,13,18,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first term is (3) and the difference is (5), so \(a_n=5n-2\). In exams, take the difference as the coefficient of (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n-2\). The first term is (3) and the difference is (5), so \(a_n=5n-2\). In exams, take the difference as the coefficient of (n).

Step 3

Exam Tip

पहला पद (3) और अंतर (5) है, इसलिए \(a_n=5n-2\) है। परीक्षा में अंतर को (n) का गुणांक मानें।

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Question 56/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

D. (28)

Step 1

Concept

\(a_5=5^2+3=28\). In exams, find the square first and then add (3).

Step 2

Why this answer is correct

The correct answer is D. (28). \(a_5=5^2+3=28\). In exams, find the square first and then add (3).

Step 3

Exam Tip

\(a_5=5^2+3=28\) है। परीक्षा में पहले वर्ग निकालें और फिर (3) जोड़ें।

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Question 57/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(4,7,12,19,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(4,7,12,19,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(n^2+3\) gives (4,7,12,19). In exams, test options by putting (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^2+3\). Using \(n^2+3\) gives (4,7,12,19). In exams, test options by putting (n=1,2,3).

Step 3

Exam Tip

\(n^2+3\) रखने पर (4,7,12,19) मिलते हैं। परीक्षा में विकल्पों में (n=1,2,3) रखकर जाँचें।

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Question 58/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=14-3n\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=14-3n\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

\(a_3=14-9=5\). In exams, subtract (3n) correctly in a decreasing formula.

Step 2

Why this answer is correct

The correct answer is B. (5). \(a_3=14-9=5\). In exams, subtract (3n) correctly in a decreasing formula.

Step 3

Exam Tip

\(a_3=14-9=5\) है। परीक्षा में घटते सूत्र में (3n) को सही घटाएँ।

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Question 59/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(11,8,5,2,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(11,8,5,2,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=14-3n\)

Step 1

Concept

At (n=1) it gives (11), and at (n=2) it gives (8), so \(a_n=14-3n\). In exams, treat a decreasing difference as negative.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=14-3n\). At (n=1) it gives (11), and at (n=2) it gives (8), so \(a_n=14-3n\). In exams, treat a decreasing difference as negative.

Step 3

Exam Tip

(n=1) पर (11) और (n=2) पर (8) मिलता है, इसलिए \(a_n=14-3n\) है। परीक्षा में घटते अंतर को ऋणात्मक समझें।

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Question 60/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=5^n\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=5^n\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(a_2=5^2=25\). In exams, identify the base and exponent separately.

Step 2

Why this answer is correct

The correct answer is C. (25). \(a_2=5^2=25\). In exams, identify the base and exponent separately.

Step 3

Exam Tip

\(a_2=5^2=25\) है। परीक्षा में आधार और घातांक को अलग पहचानें।

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Question 61/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(5,25,125,625,\ldots\) के लिए सही नियम कौन-सा है?

Which rule is correct for the sequence \(5,25,125,625,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=5^n\)

Step 1

Concept

These terms are consecutive powers of (5). In exams, check \(5^n\) when you see (5,25,125).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=5^n\). These terms are consecutive powers of (5). In exams, check \(5^n\) when you see (5,25,125).

Step 3

Exam Tip

ये पद (5) की क्रमिक घातें हैं। परीक्षा में (5,25,125) देखकर \(5^n\) जाँचें।

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Question 62/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

\(a_4=3\times4^2=48\). In exams, square first and then multiply by (3).

Step 2

Why this answer is correct

The correct answer is C. (48). \(a_4=3\times4^2=48\). In exams, square first and then multiply by (3).

Step 3

Exam Tip

\(a_4=3\times4^2=48\) है। परीक्षा में वर्ग निकालकर (3) से गुणा करें।

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Question 63/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(3,12,27,48,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,12,27,48,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

These terms come from \(3n^2\). In exams, test the square-based rule on the first three terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n^2\). These terms come from \(3n^2\). In exams, test the square-based rule on the first three terms.

Step 3

Exam Tip

ये पद \(3n^2\) से मिलते हैं। परीक्षा में वर्ग आधारित नियम को पहले तीन पदों पर जाँचें।

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Question 64/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(a_4=\frac{3\times4}{2}=6\). In exams, simplify the fraction before answering.

Step 2

Why this answer is correct

The correct answer is C. (6). \(a_4=\frac{3\times4}{2}=6\). In exams, simplify the fraction before answering.

Step 3

Exam Tip

\(a_4=\frac{3\times4}{2}=6\) है। परीक्षा में भिन्न को सरल करके उत्तर दें।

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Question 65/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(\frac{3}{2},3,\frac{9}{2},6,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(\frac{3}{2},3,\frac{9}{2},6,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Each term is the next multiple of \(\frac{3}{2}\). In exams, write fractional multiples as (kn).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=\frac{3n}{2}\). Each term is the next multiple of \(\frac{3}{2}\). In exams, write fractional multiples as (kn).

Step 3

Exam Tip

हर पद \(\frac{3}{2}\) का अगला गुणज है। परीक्षा में भिन्न गुणजों को (kn) के रूप में लिखें।

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Question 66/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=2n-3\) है, तो कौन-सा पद (15) के बराबर होगा?

If \(a_n=2n-3\), which term will be equal to (15)?

Explanation opens after your attempt

Correct Answer

C. (n=9)

Step 1

Concept

From (2n-3=15), we get (n=9). In exams, equate the formula to the given value when term number is asked.

Step 2

Why this answer is correct

The correct answer is C. (n=9). From (2n-3=15), we get (n=9). In exams, equate the formula to the given value when term number is asked.

Step 3

Exam Tip

(2n-3=15) से (n=9) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।

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Question 67/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(-1,1,3,5,\ldots\) में (15) कौन-सा पद है?

In the sequence \(-1,1,3,5,\ldots\), which term is (15)?

Explanation opens after your attempt

Correct Answer

C. नौवाँ पद(9)th term

Step 1

Concept

Its rule is \(a_n=2n-3\), and (2n-3=15) gives (n=9). In exams, form the general term first to find the term number.

Step 2

Why this answer is correct

The correct answer is C. नौवाँ पद / (9)th term. Its rule is \(a_n=2n-3\), and (2n-3=15) gives (n=9). In exams, form the general term first to find the term number.

Step 3

Exam Tip

इसका नियम \(a_n=2n-3\) है और (2n-3=15) से (n=9) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।

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Question 68/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

\(a_3=3^3=27\). In exams, multiply the number three times when finding a cube.

Step 2

Why this answer is correct

The correct answer is C. (27). \(a_3=3^3=27\). In exams, multiply the number three times when finding a cube.

Step 3

Exam Tip

\(a_3=3^3=27\) है। परीक्षा में घन निकालते समय संख्या को तीन बार गुणा करें।

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Question 69/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(1,8,27,64,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(1,8,27,64,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=n^3\)

Step 1

Concept

These are perfect cubes, so \(a_n=n^3\). In exams, recognize (1,8,27,64) as cube numbers.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^3\). These are perfect cubes, so \(a_n=n^3\). In exams, recognize (1,8,27,64) as cube numbers.

Step 3

Exam Tip

ये पूर्ण घन हैं, इसलिए \(a_n=n^3\) है। परीक्षा में (1,8,27,64) को घन संख्याओं के रूप में पहचानें।

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Question 70/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=n^3+1\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=n^3+1\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

\(a_2=2^3+1=9\). In exams, find the cube first and then add (1).

Step 2

Why this answer is correct

The correct answer is C. (9). \(a_2=2^3+1=9\). In exams, find the cube first and then add (1).

Step 3

Exam Tip

\(a_2=2^3+1=9\) है। परीक्षा में पहले घन निकालें और फिर (1) जोड़ें।

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Question 71/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(2,9,28,65,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,9,28,65,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The terms come from \(n^3+1\). In exams, check options using (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^3+1\). The terms come from \(n^3+1\). In exams, check options using (n=1,2,3).

Step 3

Exam Tip

ये पद \(n^3+1\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर विकल्प जाँचें।

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Question 72/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=20-4n\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=20-4n\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

\(a_4=20-16=4\). In exams, calculate (4n) and subtract it.

Step 2

Why this answer is correct

The correct answer is B. (4). \(a_4=20-16=4\). In exams, calculate (4n) and subtract it.

Step 3

Exam Tip

\(a_4=20-16=4\) है। परीक्षा में (4n) निकालकर उसे घटाएँ।

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Question 73/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(16,12,8,4,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(16,12,8,4,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=20-4n\)

Step 1

Concept

At (n=1) it gives (16), and at (n=2) it gives (12), so \(a_n=20-4n\). In exams, check the rule with the first term in a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=20-4n\). At (n=1) it gives (16), and at (n=2) it gives (12), so \(a_n=20-4n\). In exams, check the rule with the first term in a decreasing sequence.

Step 3

Exam Tip

(n=1) पर (16) और (n=2) पर (12) मिलता है, इसलिए \(a_n=20-4n\) है। परीक्षा में घटते अनुक्रम में पहला पद मिलाकर नियम जाँचें।

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Question 74/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=7n+1\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=7n+1\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

\(a_5=7\times5+1=36\). In exams, add the constant at the end.

Step 2

Why this answer is correct

The correct answer is C. (36). \(a_5=7\times5+1=36\). In exams, add the constant at the end.

Step 3

Exam Tip

\(a_5=7\times5+1=36\) है। परीक्षा में स्थिर संख्या को अंत में जोड़ें।

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Question 75/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(8,15,22,29,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(8,15,22,29,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=7n+1\)

Step 1

Concept

The first term is (8) and the difference is (7), so \(a_n=7n+1\). In exams, find the constant part from the first term.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=7n+1\). The first term is (8) and the difference is (7), so \(a_n=7n+1\). In exams, find the constant part from the first term.

Step 3

Exam Tip

पहला पद (8) और अंतर (7) है, इसलिए \(a_n=7n+1\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।

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Question 76/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(a_5=\frac{5\times4}{2}=10\). In exams, multiply first and then divide by (2).

Step 2

Why this answer is correct

The correct answer is B. (10). \(a_5=\frac{5\times4}{2}=10\). In exams, multiply first and then divide by (2).

Step 3

Exam Tip

\(a_5=\frac{5\times4}{2}=10\) है। परीक्षा में पहले गुणन करें और फिर (2) से भाग दें।

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Question 77/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(0,1,3,6,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(0,1,3,6,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=\frac{n(n-1)}{2})

Step 1

Concept

Putting (n=1,2,3,4) gives (0,1,3,6). In exams, test triangular-number-like options with small (n).

Step 2

Why this answer is correct

The correct answer is B. (a_n=\frac{n(n-1)}{2}). Putting (n=1,2,3,4) gives (0,1,3,6). In exams, test triangular-number-like options with small (n).

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (0,1,3,6) मिलते हैं। परीक्षा में त्रिभुज संख्या जैसे विकल्पों को छोटे (n) से जाँचें।

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Question 78/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=4n^2-1\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=4n^2-1\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (35)

Step 1

Concept

\(a_3=4\times9-1=35\). In exams, square first and then multiply by (4).

Step 2

Why this answer is correct

The correct answer is C. (35). \(a_3=4\times9-1=35\). In exams, square first and then multiply by (4).

Step 3

Exam Tip

\(a_3=4\times9-1=35\) है। परीक्षा में वर्ग के बाद (4) से गुणा करें।

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Question 79/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(3,15,35,63,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,15,35,63,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(4n^2-1\) gives (3,15,35,63). In exams, substitute (n=1,2,3) and match.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=4n^2-1\). \(4n^2-1\) gives (3,15,35,63). In exams, substitute (n=1,2,3) and match.

Step 3

Exam Tip

\(4n^2-1\) से (3,15,35,63) मिलते हैं। परीक्षा में (n=1,2,3) रखकर मिलान करें।

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Question 80/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=3n+7\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=3n+7\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(a_6=3\times6+7=25\). In exams, put the given (n) directly into the formula.

Step 2

Why this answer is correct

The correct answer is B. (25). \(a_6=3\times6+7=25\). In exams, put the given (n) directly into the formula.

Step 3

Exam Tip

\(a_6=3\times6+7=25\) है। परीक्षा में दिए (n) को सीधे सूत्र में रखें।

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Question 81/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(10,13,16,19,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(10,13,16,19,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=3n+7\)

Step 1

Concept

The difference is (3) and the first term is (10), so \(a_n=3n+7\). In exams, check the rule on the first two terms.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=3n+7\). The difference is (3) and the first term is (10), so \(a_n=3n+7\). In exams, check the rule on the first two terms.

Step 3

Exam Tip

अंतर (3) है और पहला पद (10) है, इसलिए \(a_n=3n+7\) है। परीक्षा में पहले दो पदों पर नियम जाँचें।

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Question 82/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

\(a_3=2^4=16\). In exams, find the exponent (n+1) first.

Step 2

Why this answer is correct

The correct answer is C. (16). \(a_3=2^4=16\). In exams, find the exponent (n+1) first.

Step 3

Exam Tip

\(a_3=2^4=16\) है। परीक्षा में पहले घातांक (n+1) निकालें।

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Question 83/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(4,8,16,32,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,8,16,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=2^{n+1}\)

Step 1

Concept

Using \(2^{n+1}\) gives (4,8,16,32). In exams, match power options with the first term.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=2^{n+1}\). Using \(2^{n+1}\) gives (4,8,16,32). In exams, match power options with the first term.

Step 3

Exam Tip

\(2^{n+1}\) रखने पर (4,8,16,32) मिलते हैं। परीक्षा में घात वाले विकल्पों को पहले पद से मिलाएँ।

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Question 84/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

\(a_4=16+8=24\). In exams, add both the square and (2n).

Step 2

Why this answer is correct

The correct answer is C. (24). \(a_4=16+8=24\). In exams, add both the square and (2n).

Step 3

Exam Tip

\(a_4=16+8=24\) है। परीक्षा में वर्ग और (2n) दोनों जोड़ें।

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Question 85/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(3,8,15,24,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(3,8,15,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(n^2+2n\) gives (3,8,15,24). In exams, test polynomial rules with small (n) values.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+2n\). \(n^2+2n\) gives (3,8,15,24). In exams, test polynomial rules with small (n) values.

Step 3

Exam Tip

\(n^2+2n\) से (3,8,15,24) मिलते हैं। परीक्षा में बहुपद नियमों को छोटे (n) मानों से जाँचें।

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Question 86/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=50-5n\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=50-5n\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

\(a_7=50-35=15\). In exams, subtract (5n) correctly.

Step 2

Why this answer is correct

The correct answer is B. (15). \(a_7=50-35=15\). In exams, subtract (5n) correctly.

Step 3

Exam Tip

\(a_7=50-35=15\) है। परीक्षा में (5n) को सही घटाएँ।

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Question 87/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(45,40,35,30,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(45,40,35,30,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=50-5n\)

Step 1

Concept

At (n=1), it gives (45), and at (n=2), it gives (40), so \(a_n=50-5n\). In exams, always check (n=1) when forming a decreasing rule.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=50-5n\). At (n=1), it gives (45), and at (n=2), it gives (40), so \(a_n=50-5n\). In exams, always check (n=1) when forming a decreasing rule.

Step 3

Exam Tip

(n=1) पर (45) और (n=2) पर (40) मिलता है, इसलिए \(a_n=50-5n\) है। परीक्षा में घटते समान अंतर का नियम बनाते समय (n=1) जरूर जाँचें।

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Question 88/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=6n-5\) है, तो कौन-सा पद (31) के बराबर होगा?

If \(a_n=6n-5\), which term will be equal to (31)?

Explanation opens after your attempt

Correct Answer

C. (n=6)

Step 1

Concept

From (6n-5=31), we get (n=6). In exams, equate the given term to the formula and solve.

Step 2

Why this answer is correct

The correct answer is C. (n=6). From (6n-5=31), we get (n=6). In exams, equate the given term to the formula and solve.

Step 3

Exam Tip

(6n-5=31) से (n=6) मिलता है। परीक्षा में दिए पद को सूत्र के बराबर रखकर हल करें।

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Question 89/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(1,7,13,19,\ldots\) में (31) कौन-सा पद है?

In the sequence \(1,7,13,19,\ldots\), which term is (31)?

Explanation opens after your attempt

Correct Answer

C. छठा पद(6)th term

Step 1

Concept

Its rule is \(a_n=6n-5\), and (6n-5=31) gives (n=6). In exams, form the general term to find the term number.

Step 2

Why this answer is correct

The correct answer is C. छठा पद / (6)th term. Its rule is \(a_n=6n-5\), and (6n-5=31) gives (n=6). In exams, form the general term to find the term number.

Step 3

Exam Tip

इसका नियम \(a_n=6n-5\) है और (6n-5=31) से (n=6) है। परीक्षा में सामान्य पद बनाकर पद संख्या निकालें।

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Question 90/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

\(a_5=\frac{6}{2}=3\). In exams, simplify the numerator before dividing by the denominator.

Step 2

Why this answer is correct

The correct answer is B. (3). \(a_5=\frac{6}{2}=3\). In exams, simplify the numerator before dividing by the denominator.

Step 3

Exam Tip

\(a_5=\frac{6}{2}=3\) है। परीक्षा में पहले हर में जाने से पहले अंश को सरल करें।

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Question 91/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(1,\frac{3}{2},2,\frac{5}{2},\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(1,\frac{3}{2},2,\frac{5}{2},\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(\frac{n+1}{2}\) gives \(1,\frac{3}{2},2,\frac{5}{2}\). In exams, match fractional terms using small (n) values.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=\frac{n+1}{2}\). \(\frac{n+1}{2}\) gives \(1,\frac{3}{2},2,\frac{5}{2}\). In exams, match fractional terms using small (n) values.

Step 3

Exam Tip

\(\frac{n+1}{2}\) से \(1,\frac{3}{2},2,\frac{5}{2}\) मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से मिलाएँ।

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Question 92/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=10n+5\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=10n+5\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(a_2=10\times2+5=25\). In exams, replace (n) with the term number.

Step 2

Why this answer is correct

The correct answer is C. (25). \(a_2=10\times2+5=25\). In exams, replace (n) with the term number.

Step 3

Exam Tip

\(a_2=10\times2+5=25\) है। परीक्षा में (n) की जगह पद संख्या रखें।

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Question 93/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(15,25,35,45,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(15,25,35,45,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=10n+5\)

Step 1

Concept

The first term is (15) and the difference is (10), so \(a_n=10n+5\). In exams, use the difference as the coefficient and find the constant from the first term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=10n+5\). The first term is (15) and the difference is (10), so \(a_n=10n+5\). In exams, use the difference as the coefficient and find the constant from the first term.

Step 3

Exam Tip

पहला पद (15) और अंतर (10) है, इसलिए \(a_n=10n+5\) है। परीक्षा में अंतर को गुणांक और पहले पद से स्थिर भाग निकालें।

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Question 94/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

B. (19)

Step 1

Concept

\(a_3=2\times9+1=19\). In exams, square first, multiply by (2), and add (1).

Step 2

Why this answer is correct

The correct answer is B. (19). \(a_3=2\times9+1=19\). In exams, square first, multiply by (2), and add (1).

Step 3

Exam Tip

\(a_3=2\times9+1=19\) है। परीक्षा में वर्ग के बाद (2) से गुणा करें और (1) जोड़ें।

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Question 95/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(3,9,19,33,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(3,9,19,33,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(2n^2+1\) gives (3,9,19,33). In exams, match the square-based rule with the first four terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^2+1\). Using \(2n^2+1\) gives (3,9,19,33). In exams, match the square-based rule with the first four terms.

Step 3

Exam Tip

\(2n^2+1\) रखने पर (3,9,19,33) मिलते हैं। परीक्षा में वर्ग वाले नियम को पहले चार पदों से मिलाएँ।

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Question 96/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(a_3=3^3-2=25\). In exams, find the power first and then subtract (2).

Step 2

Why this answer is correct

The correct answer is C. (25). \(a_3=3^3-2=25\). In exams, find the power first and then subtract (2).

Step 3

Exam Tip

\(a_3=3^3-2=25\) है। परीक्षा में पहले घात निकालें और फिर (2) घटाएँ।

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Question 97/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(1,7,25,79,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(1,7,25,79,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(3^n-2\) gives (1,7,25,79). In exams, also check constant subtraction in power-based options.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=3^n-2\). \(3^n-2\) gives (1,7,25,79). In exams, also check constant subtraction in power-based options.

Step 3

Exam Tip

\(3^n-2\) से (1,7,25,79) मिलते हैं। परीक्षा में घात वाले विकल्पों में स्थिर घटाव भी जाँचें।

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Question 98/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

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

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

Explanation opens after your attempt

Correct Answer

D. (24)

Step 1

Concept

\(a_6=36-12=24\). In exams, subtract (2n) from the square.

Step 2

Why this answer is correct

The correct answer is D. (24). \(a_6=36-12=24\). In exams, subtract (2n) from the square.

Step 3

Exam Tip

\(a_6=36-12=24\) है। परीक्षा में वर्ग में से (2n) घटाएँ।

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Question 99/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

अनुक्रम \(-1,0,3,8,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(-1,0,3,8,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(n^2-2n\) gives (-1,0,3,8). In exams, keep testing options even when the first term is negative.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2-2n\). \(n^2-2n\) gives (-1,0,3,8). In exams, keep testing options even when the first term is negative.

Step 3

Exam Tip

\(n^2-2n\) से (-1,0,3,8) मिलते हैं। परीक्षा में ऋणात्मक पहला पद आने पर भी विकल्पों को जाँचें।

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Question 100/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 51

यदि \(a_n=18+n\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=18+n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (23)

Step 1

Concept

\(a_5=18+5=23\). In exams, substitute directly in simple addition formulas.

Step 2

Why this answer is correct

The correct answer is C. (23). \(a_5=18+5=23\). In exams, substitute directly in simple addition formulas.

Step 3

Exam Tip

\(a_5=18+5=23\) है। परीक्षा में सरल जोड़ वाले सूत्रों में सीधे प्रतिस्थापन करें।

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Question 101/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(13,26,39,52,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(13,26,39,52,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=13n\)

Step 1

Concept

Each term is a multiple of (13), so \(a_n=13n\). In exams, check multiple-based sequences using (kn).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=13n\). Each term is a multiple of (13), so \(a_n=13n\). In exams, check multiple-based sequences using (kn).

Step 3

Exam Tip

हर पद (13) का गुणज है, इसलिए \(a_n=13n\) है। परीक्षा में गुणज वाले अनुक्रम को (kn) से जाँचें।

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Question 102/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=12n+1\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=12n+1\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(a_2=12\times2+1=25\). In exams, multiply first and then add (1).

Step 2

Why this answer is correct

The correct answer is C. (25). \(a_2=12\times2+1=25\). In exams, multiply first and then add (1).

Step 3

Exam Tip

\(a_2=12\times2+1=25\) है। परीक्षा में पहले गुणा करें और फिर (1) जोड़ें।

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Question 103/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(2,7,12,17,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(2,7,12,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=5n-3\)

Step 1

Concept

The first term is (2) and the difference is (5), so \(a_n=5n-3\). In exams, always check the first term by putting (n=1).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=5n-3\). The first term is (2) and the difference is (5), so \(a_n=5n-3\). In exams, always check the first term by putting (n=1).

Step 3

Exam Tip

पहला पद (2) और अंतर (5) है, इसलिए \(a_n=5n-3\) है। परीक्षा में (n=1) रखकर पहला पद जरूर जाँचें।

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Question 104/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=8n+6\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=8n+6\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (30)

Step 1

Concept

\(a_3=8\times3+6=30\). In exams, put the term number directly into the formula.

Step 2

Why this answer is correct

The correct answer is B. (30). \(a_3=8\times3+6=30\). In exams, put the term number directly into the formula.

Step 3

Exam Tip

\(a_3=8\times3+6=30\) है। परीक्षा में पद संख्या को सीधे सूत्र में रखें।

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Question 105/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(14,20,26,32,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(14,20,26,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=6n+8\)

Step 1

Concept

The difference is (6) and the first term is (14), so \(a_n=6n+8\). In exams, take the difference as the coefficient of (n).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=6n+8\). The difference is (6) and the first term is (14), so \(a_n=6n+8\). In exams, take the difference as the coefficient of (n).

Step 3

Exam Tip

अंतर (6) है और पहला पद (14) है, इसलिए \(a_n=6n+8\) है। परीक्षा में अंतर को (n) का गुणांक मानें।

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Question 106/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(a_4=4^2+4=20\). In exams, find the square first and then add (4).

Step 2

Why this answer is correct

The correct answer is C. (20). \(a_4=4^2+4=20\). In exams, find the square first and then add (4).

Step 3

Exam Tip

\(a_4=4^2+4=20\) है। परीक्षा में पहले वर्ग निकालें और फिर (4) जोड़ें।

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Question 107/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(5,8,13,20,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(5,8,13,20,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(n^2+4\) gives (5,8,13,20). In exams, match options using (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^2+4\). Using \(n^2+4\) gives (5,8,13,20). In exams, match options using (n=1,2,3).

Step 3

Exam Tip

\(n^2+4\) रखने पर (5,8,13,20) मिलते हैं। परीक्षा में विकल्पों को (n=1,2,3) से मिलाएँ।

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Question 108/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=30-2n\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=30-2n\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

\(a_7=30-14=16\). In exams, subtract (2n) correctly in a decreasing formula.

Step 2

Why this answer is correct

The correct answer is C. (16). \(a_7=30-14=16\). In exams, subtract (2n) correctly in a decreasing formula.

Step 3

Exam Tip

\(a_7=30-14=16\) है। परीक्षा में घटते सूत्र में (2n) को सही घटाएँ।

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Question 109/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(28,26,24,22,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(28,26,24,22,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=30-2n\)

Step 1

Concept

At (n=1) it gives (28), and at (n=2) it gives (26), so \(a_n=30-2n\). In exams, treat a decreasing difference as negative.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=30-2n\). At (n=1) it gives (28), and at (n=2) it gives (26), so \(a_n=30-2n\). In exams, treat a decreasing difference as negative.

Step 3

Exam Tip

(n=1) पर (28) और (n=2) पर (26) मिलता है, इसलिए \(a_n=30-2n\) है। परीक्षा में घटते अंतर को ऋणात्मक मानें।

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Question 110/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=4^n\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=4^n\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

\(a_2=4^2=16\). In exams, identify the base and exponent separately.

Step 2

Why this answer is correct

The correct answer is C. (16). \(a_2=4^2=16\). In exams, identify the base and exponent separately.

Step 3

Exam Tip

\(a_2=4^2=16\) है। परीक्षा में आधार और घातांक को अलग पहचानें।

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Question 111/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(4,16,64,256,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(4,16,64,256,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=4^n\)

Step 1

Concept

These terms are consecutive powers of (4). In exams, check power rules in rapidly growing sequences.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=4^n\). These terms are consecutive powers of (4). In exams, check power rules in rapidly growing sequences.

Step 3

Exam Tip

ये पद (4) की क्रमिक घातें हैं। परीक्षा में तेज बढ़ते अनुक्रमों में घात वाले नियम जाँचें।

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Question 112/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

B. (22)

Step 1

Concept

\(a_2=5\times4+2=22\). In exams, square first and then multiply by (5).

Step 2

Why this answer is correct

The correct answer is B. (22). \(a_2=5\times4+2=22\). In exams, square first and then multiply by (5).

Step 3

Exam Tip

\(a_2=5\times4+2=22\) है। परीक्षा में वर्ग निकालकर (5) से गुणा करें।

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Question 113/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(7,22,47,82,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(7,22,47,82,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(5n^2+2\) gives (7,22,47,82). In exams, test square-based rules with small (n) values.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=5n^2+2\). \(5n^2+2\) gives (7,22,47,82). In exams, test square-based rules with small (n) values.

Step 3

Exam Tip

\(5n^2+2\) से (7,22,47,82) मिलते हैं। परीक्षा में वर्ग आधारित नियमों को छोटे (n) मानों से जाँचें।

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Question 114/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

\(a_6=\frac{5\times6}{2}=15\). In exams, simplify the fraction before answering.

Step 2

Why this answer is correct

The correct answer is C. (15). \(a_6=\frac{5\times6}{2}=15\). In exams, simplify the fraction before answering.

Step 3

Exam Tip

\(a_6=\frac{5\times6}{2}=15\) है। परीक्षा में भिन्न को सरल करके उत्तर दें।

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Question 115/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(\frac{5}{2},5,\frac{15}{2},10,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(\frac{5}{2},5,\frac{15}{2},10,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Each term is the next multiple of \(\frac{5}{2}\). In exams, write fractional multiples as (kn).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{5n}{2}\). Each term is the next multiple of \(\frac{5}{2}\). In exams, write fractional multiples as (kn).

Step 3

Exam Tip

हर पद \(\frac{5}{2}\) का अगला गुणज है। परीक्षा में भिन्न गुणजों को (kn) के रूप में लिखें।

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Question 116/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=4n-7\) है, तो कौन-सा पद (25) के बराबर होगा?

If \(a_n=4n-7\), which term will be equal to (25)?

Explanation opens after your attempt

Correct Answer

C. (n=8)

Step 1

Concept

From (4n-7=25), we get (n=8). In exams, when the term number is asked, equate the formula to the given value.

Step 2

Why this answer is correct

The correct answer is C. (n=8). From (4n-7=25), we get (n=8). In exams, when the term number is asked, equate the formula to the given value.

Step 3

Exam Tip

(4n-7=25) से (n=8) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें।

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Question 117/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(-3,1,5,9,\ldots\) में (25) कौन-सा पद है?

In the sequence \(-3,1,5,9,\ldots\), which term is (25)?

Explanation opens after your attempt

Correct Answer

C. आठवाँ पद(8)th term

Step 1

Concept

Its rule is \(a_n=4n-7\), and (4n-7=25) gives (n=8). In exams, form the general term first to find the term number.

Step 2

Why this answer is correct

The correct answer is C. आठवाँ पद / (8)th term. Its rule is \(a_n=4n-7\), and (4n-7=25) gives (n=8). In exams, form the general term first to find the term number.

Step 3

Exam Tip

इसका नियम \(a_n=4n-7\) है और (4n-7=25) से (n=8) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें।

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Question 118/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (26)

Step 1

Concept

\(a_3=3^3-1=26\). In exams, find the cube first and then subtract (1).

Step 2

Why this answer is correct

The correct answer is C. (26). \(a_3=3^3-1=26\). In exams, find the cube first and then subtract (1).

Step 3

Exam Tip

\(a_3=3^3-1=26\) है। परीक्षा में पहले घन निकालें और फिर (1) घटाएँ।

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Question 119/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(0,7,26,63,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(0,7,26,63,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(n^3-1\) gives (0,7,26,63). In exams, match cube-based options with the first four terms.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=n^3-1\). \(n^3-1\) gives (0,7,26,63). In exams, match cube-based options with the first four terms.

Step 3

Exam Tip

\(n^3-1\) से (0,7,26,63) मिलते हैं। परीक्षा में घन वाले विकल्पों को पहले चार पदों से मिलाएँ।

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Question 120/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

\(a_2=2\times2^3=16\). In exams, cube first and then multiply by (2).

Step 2

Why this answer is correct

The correct answer is C. (16). \(a_2=2\times2^3=16\). In exams, cube first and then multiply by (2).

Step 3

Exam Tip

\(a_2=2\times2^3=16\) है। परीक्षा में घन के बाद (2) से गुणा करें।

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Question 121/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(2,16,54,128,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(2,16,54,128,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

These terms come from \(2n^3\). In exams, check the rule by putting (n=1,2,3).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=2n^3\). These terms come from \(2n^3\). In exams, check the rule by putting (n=1,2,3).

Step 3

Exam Tip

ये पद \(2n^3\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर नियम जाँचें।

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Question 122/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=40-3n\) है, तो \(a_5\) का मान क्या होगा?

If \(a_n=40-3n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(a_5=40-15=25\). In exams, subtract (3n) correctly.

Step 2

Why this answer is correct

The correct answer is C. (25). \(a_5=40-15=25\). In exams, subtract (3n) correctly.

Step 3

Exam Tip

\(a_5=40-15=25\) है। परीक्षा में (3n) को सही घटाएँ।

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Question 123/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(37,34,31,28,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(37,34,31,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=40-3n\)

Step 1

Concept

At (n=1) it gives (37), and at (n=2) it gives (34), so \(a_n=40-3n\). In exams, check a decreasing rule with the first term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=40-3n\). At (n=1) it gives (37), and at (n=2) it gives (34), so \(a_n=40-3n\). In exams, check a decreasing rule with the first term.

Step 3

Exam Tip

(n=1) पर (37) और (n=2) पर (34) मिलता है, इसलिए \(a_n=40-3n\) है। परीक्षा में घटते नियम को पहले पद से जाँचें।

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Question 124/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=9n+2\) है, तो \(a_4\) का मान क्या होगा?

If \(a_n=9n+2\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

\(a_4=9\times4+2=38\). In exams, add the constant at the end.

Step 2

Why this answer is correct

The correct answer is C. (38). \(a_4=9\times4+2=38\). In exams, add the constant at the end.

Step 3

Exam Tip

\(a_4=9\times4+2=38\) है। परीक्षा में स्थिर संख्या को अंत में जोड़ें।

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Question 125/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(11,20,29,38,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(11,20,29,38,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=9n+2\)

Step 1

Concept

The first term is (11) and the difference is (9), so \(a_n=9n+2\). In exams, check the rule on the first two terms.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=9n+2\). The first term is (11) and the difference is (9), so \(a_n=9n+2\). In exams, check the rule on the first two terms.

Step 3

Exam Tip

पहला पद (11) और अंतर (9) है, इसलिए \(a_n=9n+2\) है। परीक्षा में पहले दो पदों पर नियम जाँचें।

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Question 126/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

\(a_3=\frac{3\times6}{2}=9\). In exams, find (n+3) first and then simplify.

Step 2

Why this answer is correct

The correct answer is C. (9). \(a_3=\frac{3\times6}{2}=9\). In exams, find (n+3) first and then simplify.

Step 3

Exam Tip

\(a_3=\frac{3\times6}{2}=9\) है। परीक्षा में पहले (n+3) निकालें और फिर सरल करें।

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Question 127/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(2,5,9,14,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(2,5,9,14,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(\frac{n(n+3)}{2}) gives (2,5,9,14). In exams, test fractional formulas with small (n) values.

Step 2

Why this answer is correct

The correct answer is B. (a_n=\frac{n(n+3)}{2}). (\frac{n(n+3)}{2}) gives (2,5,9,14). In exams, test fractional formulas with small (n) values.

Step 3

Exam Tip

(\frac{n(n+3)}{2}) से (2,5,9,14) मिलते हैं। परीक्षा में भिन्न सूत्रों को छोटे (n) मानों से जाँचें।

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Question 128/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

B. (22)

Step 1

Concept

\(a_2=6\times4-2=22\). In exams, square first, multiply by (6), and subtract (2).

Step 2

Why this answer is correct

The correct answer is B. (22). \(a_2=6\times4-2=22\). In exams, square first, multiply by (6), and subtract (2).

Step 3

Exam Tip

\(a_2=6\times4-2=22\) है। परीक्षा में वर्ग के बाद (6) से गुणा करें और (2) घटाएँ।

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Question 129/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(4,22,52,94,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(4,22,52,94,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(6n^2-2\) gives (4,22,52,94). In exams, match the square rule with the first three terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=6n^2-2\). Using \(6n^2-2\) gives (4,22,52,94). In exams, match the square rule with the first three terms.

Step 3

Exam Tip

\(6n^2-2\) रखने पर (4,22,52,94) मिलते हैं। परीक्षा में वर्ग वाले नियम को पहले तीन पदों से मिलाएँ।

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Question 130/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=4n+9\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=4n+9\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (33)

Step 1

Concept

\(a_6=4\times6+9=33\). In exams, put the given (n) directly into the formula.

Step 2

Why this answer is correct

The correct answer is B. (33). \(a_6=4\times6+9=33\). In exams, put the given (n) directly into the formula.

Step 3

Exam Tip

\(a_6=4\times6+9=33\) है। परीक्षा में दिए (n) को सीधे सूत्र में रखें।

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Question 131/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(13,17,21,25,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(13,17,21,25,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=4n+9\)

Step 1

Concept

The difference is (4) and the first term is (13), so \(a_n=4n+9\). In exams, match both the difference and the first term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=4n+9\). The difference is (4) and the first term is (13), so \(a_n=4n+9\). In exams, match both the difference and the first term.

Step 3

Exam Tip

अंतर (4) है और पहला पद (13) है, इसलिए \(a_n=4n+9\) है। परीक्षा में अंतर और पहला पद दोनों मिलाएँ।

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Question 132/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=3^{n+1}\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=3^{n+1}\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

\(a_2=3^3=27\). In exams, find the exponent (n+1) first.

Step 2

Why this answer is correct

The correct answer is C. (27). \(a_2=3^3=27\). In exams, find the exponent (n+1) first.

Step 3

Exam Tip

\(a_2=3^3=27\) है। परीक्षा में पहले घातांक (n+1) निकालें।

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Question 133/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(9,27,81,243,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(9,27,81,243,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_n=3^{n+1}\)

Step 1

Concept

\(3^{n+1}\) gives (9,27,81,243). In exams, use the first term to identify the exponent shift.

Step 2

Why this answer is correct

The correct answer is C. \(a_n=3^{n+1}\). \(3^{n+1}\) gives (9,27,81,243). In exams, use the first term to identify the exponent shift.

Step 3

Exam Tip

\(3^{n+1}\) से (9,27,81,243) मिलते हैं। परीक्षा में पहले पद देखकर घातांक का बदलाव पहचानें।

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Question 134/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

B. (28)

Step 1

Concept

\(a_4=16+12=28\). In exams, add both the square and (3n).

Step 2

Why this answer is correct

The correct answer is B. (28). \(a_4=16+12=28\). In exams, add both the square and (3n).

Step 3

Exam Tip

\(a_4=16+12=28\) है। परीक्षा में वर्ग और (3n) दोनों जोड़ें।

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Question 135/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(4,10,18,28,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(4,10,18,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using \(n^2+3n\) gives (4,10,18,28). In exams, test the polynomial rule with the first four terms.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2+3n\). Using \(n^2+3n\) gives (4,10,18,28). In exams, test the polynomial rule with the first four terms.

Step 3

Exam Tip

\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। परीक्षा में बहुपद नियम को पहले चार पदों से जाँचें।

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Question 136/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=60-6n\) है, तो \(a_8\) का मान क्या होगा?

If \(a_n=60-6n\), what is the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

\(a_8=60-48=12\). In exams, subtract (6n) correctly.

Step 2

Why this answer is correct

The correct answer is B. (12). \(a_8=60-48=12\). In exams, subtract (6n) correctly.

Step 3

Exam Tip

\(a_8=60-48=12\) है। परीक्षा में (6n) को सही घटाएँ।

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Question 137/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(54,48,42,36,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(54,48,42,36,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=60-6n\)

Step 1

Concept

At (n=1) it gives (54), and at (n=2) it gives (48), so \(a_n=60-6n\). In exams, check a decreasing sequence rule using (n=1).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=60-6n\). At (n=1) it gives (54), and at (n=2) it gives (48), so \(a_n=60-6n\). In exams, check a decreasing sequence rule using (n=1).

Step 3

Exam Tip

(n=1) पर (54) और (n=2) पर (48) मिलता है, इसलिए \(a_n=60-6n\) है। परीक्षा में घटते अनुक्रम में (n=1) से नियम जाँचें।

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Question 138/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=7n-8\) है, तो कौन-सा पद (41) के बराबर होगा?

If \(a_n=7n-8\), which term will be equal to (41)?

Explanation opens after your attempt

Correct Answer

C. (n=7)

Step 1

Concept

From (7n-8=41), we get (n=7). In exams, equate the given value to the formula and solve.

Step 2

Why this answer is correct

The correct answer is C. (n=7). From (7n-8=41), we get (n=7). In exams, equate the given value to the formula and solve.

Step 3

Exam Tip

(7n-8=41) से (n=7) मिलता है। परीक्षा में दिए मान को सूत्र के बराबर रखकर हल करें।

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Question 139/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(-1,6,13,20,\ldots\) में (41) कौन-सा पद है?

In the sequence \(-1,6,13,20,\ldots\), which term is (41)?

Explanation opens after your attempt

Correct Answer

C. सातवाँ पद(7)th term

Step 1

Concept

Its rule is \(a_n=7n-8\), and (7n-8=41) gives (n=7). In exams, find the term number from the general term.

Step 2

Why this answer is correct

The correct answer is C. सातवाँ पद / (7)th term. Its rule is \(a_n=7n-8\), and (7n-8=41) gives (n=7). In exams, find the term number from the general term.

Step 3

Exam Tip

इसका नियम \(a_n=7n-8\) है और (7n-8=41) से (n=7) है। परीक्षा में सामान्य पद से पद संख्या निकालें।

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Question 140/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

If \(a_n=\frac{2n+1}{3}\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

\(a_4=\frac{9}{3}=3\). In exams, simplify the numerator first and then divide.

Step 2

Why this answer is correct

The correct answer is B. (3). \(a_4=\frac{9}{3}=3\). In exams, simplify the numerator first and then divide.

Step 3

Exam Tip

\(a_4=\frac{9}{3}=3\) है। परीक्षा में पहले अंश को सरल करें और फिर भाग दें।

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Question 141/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(1,\frac{5}{3},\frac{7}{3},3,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(1,\frac{5}{3},\frac{7}{3},3,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(\frac{2n+1}{3}\) gives \(1,\frac{5}{3},\frac{7}{3},3\). In exams, match fractional rules with small (n) values.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=\frac{2n+1}{3}\). \(\frac{2n+1}{3}\) gives \(1,\frac{5}{3},\frac{7}{3},3\). In exams, match fractional rules with small (n) values.

Step 3

Exam Tip

\(\frac{2n+1}{3}\) से \(1,\frac{5}{3},\frac{7}{3},3\) मिलते हैं। परीक्षा में भिन्न नियमों को छोटे (n) मानों से मिलाएँ।

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Question 142/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=11n+4\) है, तो \(a_3\) का मान क्या होगा?

If \(a_n=11n+4\), what is the value of \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (37)

Step 1

Concept

\(a_3=11\times3+4=37\). In exams, multiply first and then add the constant.

Step 2

Why this answer is correct

The correct answer is B. (37). \(a_3=11\times3+4=37\). In exams, multiply first and then add the constant.

Step 3

Exam Tip

\(a_3=11\times3+4=37\) है। परीक्षा में गुणा के बाद स्थिर संख्या जोड़ें।

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Question 143/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(15,26,37,48,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which general term is correct for the sequence \(15,26,37,48,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=11n+4\)

Step 1

Concept

The first term is (15) and the difference is (11), so \(a_n=11n+4\). In exams, use the difference as coefficient and find the constant from the first term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=11n+4\). The first term is (15) and the difference is (11), so \(a_n=11n+4\). In exams, use the difference as coefficient and find the constant from the first term.

Step 3

Exam Tip

पहला पद (15) और अंतर (11) है, इसलिए \(a_n=11n+4\) है। परीक्षा में अंतर को गुणांक और पहले पद से स्थिर भाग निकालें।

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Question 144/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (33)

Step 1

Concept

\(a_3=3\times9+6=33\). In exams, add both the square part and the linear part.

Step 2

Why this answer is correct

The correct answer is C. (33). \(a_3=3\times9+6=33\). In exams, add both the square part and the linear part.

Step 3

Exam Tip

\(a_3=3\times9+6=33\) है। परीक्षा में वर्ग वाला भाग और रैखिक भाग दोनों जोड़ें।

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Question 145/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(5,16,33,56,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(5,16,33,56,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(3n^2+2n\) gives (5,16,33,56). In exams, substitute (n=1,2,3) and match.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=3n^2+2n\). \(3n^2+2n\) gives (5,16,33,56). In exams, substitute (n=1,2,3) and match.

Step 3

Exam Tip

\(3n^2+2n\) से (5,16,33,56) मिलते हैं। परीक्षा में (n=1,2,3) रखकर मिलान करें।

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Question 146/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

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

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

Explanation opens after your attempt

Correct Answer

C. (19)

Step 1

Concept

\(a_4=2^4+3=19\). In exams, find the power first and then add (3).

Step 2

Why this answer is correct

The correct answer is C. (19). \(a_4=2^4+3=19\). In exams, find the power first and then add (3).

Step 3

Exam Tip

\(a_4=2^4+3=19\) है। परीक्षा में पहले घात निकालें और फिर (3) जोड़ें।

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Question 147/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(5,7,11,19,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Which explicit rule is correct for the sequence \(5,7,11,19,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(2^n+3\) gives (5,7,11,19). In exams, also check constant addition in power-based options.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=2^n+3\). \(2^n+3\) gives (5,7,11,19). In exams, also check constant addition in power-based options.

Step 3

Exam Tip

\(2^n+3\) से (5,7,11,19) मिलते हैं। परीक्षा में घात वाले विकल्पों में स्थिर जोड़ भी जाँचें।

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Question 148/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

यदि \(a_n=n^2-3n\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=n^2-3n\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

C. (28)

Step 1

Concept

\(a_7=49-21=28\). In exams, subtract (3n) from the square.

Step 2

Why this answer is correct

The correct answer is C. (28). \(a_7=49-21=28\). In exams, subtract (3n) from the square.

Step 3

Exam Tip

\(a_7=49-21=28\) है। परीक्षा में वर्ग में से (3n) घटाएँ।

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Question 149/150 Easy Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 52

अनुक्रम \(-2,-2,0,4,\ldots\) का सामान्य पद क्या है?

What is the general term of the sequence \(-2,-2,0,4,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(n^2-3n\) gives (-2,-2,0,4). In exams, do not reject a rule just because terms are zero or negative.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2-3n\). \(n^2-3n\) gives (-2,-2,0,4). In exams, do not reject a rule just because terms are zero or negative.

Step 3

Exam Tip

\(n^2-3n\) से (-2,-2,0,4) मिलते हैं। परीक्षा में शून्य या ऋणात्मक पद देखकर नियम को न छोड़ें।

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

यदि \(a_n=25+n\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=25+n\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

\(a_6=25+6=31\). In exams, substitute directly in simple addition formulas.

Step 2

Why this answer is correct

The correct answer is C. (31). \(a_6=25+6=31\). In exams, substitute directly in simple addition formulas.

Step 3

Exam Tip

\(a_6=25+6=31\) है। परीक्षा में सरल जोड़ वाले सूत्रों में सीधे प्रतिस्थापन करें।

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Class 9 Mathematics - Sequences and Progressions - Explicit or general rule Easy Quiz

अनुक्रम \(3,6,9,12,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(5,10,15,20,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(2,4,6,8,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(1,3,5,7,\ldots\) का स्पष्ट नियम कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=n^2\) है, तो अनुक्रम के पहले तीन पद क्या होंगे?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(4,7,10,13,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(10,20,30,40,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=7n\) है, तो \(a_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=n+9\) है, तो अनुक्रम का पहला पद क्या है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(9,18,27,36,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(7,14,21,28,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=2n+5\) है, तो \(a_1\) और \(a_2\) क्या होंगे?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(12,15,18,21,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=6n-1\) है, तो \(a_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(1,4,9,16,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(2,5,10,17,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Concept

Why this answer is correct