Class 9 Mathematics - Sequences and Progressions - nth term Medium Quiz

Mathematics Sequences and Progressions nth term Medium Class 9 Level 58

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Question 1/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(8,14,20,26,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(8,14,20,26,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (6n+2)

Step 1

Concept

The first term is (8) and the common difference is (6), so (a_n=8+(n-1)6=6n+2). Check the rule by putting (n=1).

Step 2

Why this answer is correct

The correct answer is B. (6n+2). The first term is (8) and the common difference is (6), so (a_n=8+(n-1)6=6n+2). Check the rule by putting (n=1).

Step 3

Exam Tip

पहला पद (8) और समान अंतर (6) है, इसलिए (a_n=8+(n-1)6=6n+2)। पहले पद पर (n=1) रखकर नियम जांचें।

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Question 2/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=5n+4\) है, तो \(a_{10}\) का मान क्या होगा?

If \(a_n=5n+4\), what is the value of \(a_{10}\)?

Explanation opens after your attempt
Correct Answer

C. (54)

Step 1

Concept

(a_{10}=5(10)+4=54). Substitute the term number for (n) in the given rule.

Step 2

Why this answer is correct

The correct answer is C. (54). (a_{10}=5(10)+4=54). Substitute the term number for (n) in the given rule.

Step 3

Exam Tip

(a_{10}=5(10)+4=54)। दिए नियम में (n) की जगह पद-संख्या रखें।

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Question 3/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

समानांतर श्रेढ़ी में पहला पद (11) और समान अंतर (3) है। (16)वाँ पद क्या होगा?

In an arithmetic progression, the first term is (11) and the common difference is (3). What is the (16)th term?

Explanation opens after your attempt
Correct Answer

B. (56)

Step 1

Concept

(a_{16}=11+15(3)=56). Up to the (16)th term, (15) common differences are used.

Step 2

Why this answer is correct

The correct answer is B. (56). (a_{16}=11+15(3)=56). Up to the (16)th term, (15) common differences are used.

Step 3

Exam Tip

(a_{16}=11+15(3)=56)। (16)वें पद तक (15) समान अंतर लगते हैं।

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Question 4/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(6,12,24,\ldots\) का (7)वाँ पद क्या है?

What is the (7)th term of the geometric progression \(6,12,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (384)

Step 1

Concept

Here (r=2), so \(a_7=6\cdot2^6=384\). Use \(a_n=ar^{n-1}\) in a geometric progression.

Step 2

Why this answer is correct

The correct answer is C. (384). Here (r=2), so \(a_7=6\cdot2^6=384\). Use \(a_n=ar^{n-1}\) in a geometric progression.

Step 3

Exam Tip

यहाँ (r=2), इसलिए \(a_7=6\cdot2^6=384\)। गुणोत्तर श्रेढ़ी में \(a_n=ar^{n-1}\) लगाएं।

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Question 5/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(6,9,14,21,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(6,9,14,21,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+5\)

Step 1

Concept

The terms are \(1^2+5,2^2+5,3^2+5,\ldots\), so \(a_n=n^2+5\). Identify the square plus a constant.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+5\). The terms are \(1^2+5,2^2+5,3^2+5,\ldots\), so \(a_n=n^2+5\). Identify the square plus a constant.

Step 3

Exam Tip

पद \(1^2+5,2^2+5,3^2+5,\ldots\) हैं, इसलिए \(a_n=n^2+5\)। वर्ग के साथ स्थिर जोड़ पहचानें।

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Question 6/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=4n^2+3\) है, तो \(a_5\) क्या होगा?

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

Explanation opens after your attempt
Correct Answer

C. (103)

Step 1

Concept

(a_5=4(5)2+3=103). Square first, then multiply and add.

Step 2

Why this answer is correct

The correct answer is C. (103). (a_5=4(5)2+3=103). Square first, then multiply and add.

Step 3

Exam Tip

(a_5=4(5)2+3=103)। पहले वर्ग करें फिर गुणा और जोड़ करें।

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Question 7/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(7,13,19,25,\ldots\) में (61) कौन-सा पद है?

In the sequence \(7,13,19,25,\ldots\), which term is (61)?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Step 1

Concept

(a_n=7+(n-1)6=6n+1), so (6n+1=61) gives (n=10). Set the rule equal to the given term to find its position.

Step 2

Why this answer is correct

The correct answer is C. (10)वाँ / (10)th. (a_n=7+(n-1)6=6n+1), so (6n+1=61) gives (n=10). Set the rule equal to the given term to find its position.

Step 3

Exam Tip

(a_n=7+(n-1)6=6n+1), इसलिए (6n+1=61) से (n=10)। दिए पद की स्थिति के लिए नियम को बराबर रखें।

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Question 8/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=7n-1\) है, तो कौन-सा पद (69) के बराबर होगा?

If \(a_n=7n-1\), which term will be equal to (69)?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Step 1

Concept

From (7n-1=69), (7n=70) and (n=10). Solve the equation to find the term position.

Step 2

Why this answer is correct

The correct answer is C. (10)वाँ / (10)th. From (7n-1=69), (7n=70) and (n=10). Solve the equation to find the term position.

Step 3

Exam Tip

(7n-1=69) से (7n=70) और (n=10)। पद की स्थिति निकालने के लिए समीकरण हल करें।

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Question 9/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(5,12,19,26,\ldots\) का (13)वाँ पद क्या है?

What is the (13)th term of the sequence \(5,12,19,26,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (89)

Step 1

Concept

(a_{13}=5+12(7)=89). Up to the (13)th term, (12) common differences are used.

Step 2

Why this answer is correct

The correct answer is C. (89). (a_{13}=5+12(7)=89). Up to the (13)th term, (12) common differences are used.

Step 3

Exam Tip

(a_{13}=5+12(7)=89)। (13)वें पद तक (12) समान अंतर लगते हैं।

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Question 10/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(7,21,63,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the geometric progression \(7,21,63,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(7\cdot3^{n-1}\)

Step 1

Concept

The first term is (7) and the ratio is (3), so \(a_n=7\cdot3^{n-1}\). In the geometric rule, the exponent is (n-1).

Step 2

Why this answer is correct

The correct answer is A. \(7\cdot3^{n-1}\). The first term is (7) and the ratio is (3), so \(a_n=7\cdot3^{n-1}\). In the geometric rule, the exponent is (n-1).

Step 3

Exam Tip

पहला पद (7) और अनुपात (3) है, इसलिए \(a_n=7\cdot3^{n-1}\)। गुणोत्तर नियम में घात (n-1) होती है।

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Question 11/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

B. (70)

Step 1

Concept

(a_7=72+3(7)=70). Do the square and multiplication in order.

Step 2

Why this answer is correct

The correct answer is B. (70). (a_7=72+3(7)=70). Do the square and multiplication in order.

Step 3

Exam Tip

(a_7=72+3(7)=70)। वर्ग और गुणा को क्रम से करें।

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Question 12/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

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

Explanation opens after your attempt
Correct Answer

A. (26-5n)

Step 1

Concept

The first term is (21) and the difference is (-5), so (a_n=21+(n-1)(-5)=26-5n). In a decreasing sequence, the difference is negative.

Step 2

Why this answer is correct

The correct answer is A. (26-5n). The first term is (21) and the difference is (-5), so (a_n=21+(n-1)(-5)=26-5n). In a decreasing sequence, the difference is negative.

Step 3

Exam Tip

पहला पद (21) और अंतर (-5) है, इसलिए (a_n=21+(n-1)(-5)=26-5n)। घटती श्रेढ़ी में अंतर ऋणात्मक होता है।

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Question 13/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=55-4n\) है, तो \(a_{11}\) क्या होगा?

If \(a_n=55-4n\), what is \(a_{11}\)?

Explanation opens after your attempt
Correct Answer

C. (11)

Step 1

Concept

(a_{11}=55-4(11)=11). Be careful with subtraction in a decreasing rule.

Step 2

Why this answer is correct

The correct answer is C. (11). (a_{11}=55-4(11)=11). Be careful with subtraction in a decreasing rule.

Step 3

Exam Tip

(a_{11}=55-4(11)=11)। घटते नियम में घटाव सावधानी से करें।

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Question 14/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=10n+1\) है, तो \(a_8-a_3\) कितना होगा?

If \(a_n=10n+1\), what is \(a_8-a_3\)?

Explanation opens after your attempt
Correct Answer

C. (50)

Step 1

Concept

\(a_8=81\) and \(a_3=31\), so the difference is (50). Find both terms separately and subtract.

Step 2

Why this answer is correct

The correct answer is C. (50). \(a_8=81\) and \(a_3=31\), so the difference is (50). Find both terms separately and subtract.

Step 3

Exam Tip

\(a_8=81\) और \(a_3=31\), इसलिए अंतर (50) है। दोनों पद अलग निकालकर घटाएं।

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Question 15/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(10,17,24,31,\ldots\) में कौन-सा पद (73) है?

In the sequence \(10,17,24,31,\ldots\), which term is (73)?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Step 1

Concept

(a_n=10+(n-1)7=7n+3), so (7n+3=73) gives (n=10). Form the rule and set it equal to the given term.

Step 2

Why this answer is correct

The correct answer is C. (10)वाँ / (10)th. (a_n=10+(n-1)7=7n+3), so (7n+3=73) gives (n=10). Form the rule and set it equal to the given term.

Step 3

Exam Tip

(a_n=10+(n-1)7=7n+3), इसलिए (7n+3=73) से (n=10)। नियम बनाकर दिए पद के बराबर रखें।

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Question 16/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=6^n\) है, तो \(a_3\) क्या होगा?

If \(a_n=6^n\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (216)

Step 1

Concept

\(a_3=6^3=216\). In an exponential rule, keep the base and exponent correct.

Step 2

Why this answer is correct

The correct answer is C. (216). \(a_3=6^3=216\). In an exponential rule, keep the base and exponent correct.

Step 3

Exam Tip

\(a_3=6^3=216\)। घातांक वाले नियम में आधार और घात सही रखें।

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Question 17/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(8,13,20,29,\ldots\) के लिए सही (n)वाँ पद कौन-सा है?

Which is the correct (n)th term for the sequence \(8,13,20,29,\ldots\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Putting \(n^2+2n+5\) gives (8,13,20,29). Check the rule on the first few terms.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+2n+5\). Putting \(n^2+2n+5\) gives (8,13,20,29). Check the rule on the first few terms.

Step 3

Exam Tip

\(n^2+2n+5\) रखने पर (8,13,20,29) मिलते हैं। पहले कुछ पदों पर नियम जांचें।

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Question 18/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=6n+11\) है, तो \(a_6+a_4\) का मान क्या है?

If \(a_n=6n+11\), what is the value of \(a_6+a_4\)?

Explanation opens after your attempt
Correct Answer

B. (82)

Step 1

Concept

\(a_6=47\) and \(a_4=35\), so the sum is (82). Find both terms separately for the correct sum.

Step 2

Why this answer is correct

The correct answer is B. (82). \(a_6=47\) and \(a_4=35\), so the sum is (82). Find both terms separately for the correct sum.

Step 3

Exam Tip

\(a_6=47\) और \(a_4=35\), इसलिए योग (82) है। सही योग के लिए दोनों पद अलग निकालें।

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Question 19/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(16,22,28,34,\ldots\) का (17)वाँ पद क्या है?

What is the (17)th term of the sequence \(16,22,28,34,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (112)

Step 1

Concept

(a_{17}=16+16(6)=112). Up to the (17)th term, (16) common differences are used.

Step 2

Why this answer is correct

The correct answer is C. (112). (a_{17}=16+16(6)=112). Up to the (17)th term, (16) common differences are used.

Step 3

Exam Tip

(a_{17}=16+16(6)=112)। (17)वें पद तक (16) समान अंतर लगते हैं।

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Question 20/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=7^n\) है, तो \(a_2\) क्या होगा?

If \(a_n=7^n\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

C. (49)

Step 1

Concept

\(a_2=7^2=49\). Put (2) in place of (n) in the exponential term.

Step 2

Why this answer is correct

The correct answer is C. (49). \(a_2=7^2=49\). Put (2) in place of (n) in the exponential term.

Step 3

Exam Tip

\(a_2=7^2=49\)। घात वाले पद में (n) की जगह (2) रखें।

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Question 21/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(5,7,9,11,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(5,7,9,11,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (2n+3)

Step 1

Concept

These are odd numbers starting from (5), so \(a_n=2n+3\). For (n=1), the first term should be (5).

Step 2

Why this answer is correct

The correct answer is B. (2n+3). These are odd numbers starting from (5), so \(a_n=2n+3\). For (n=1), the first term should be (5).

Step 3

Exam Tip

यह (5) से शुरू होने वाली विषम संख्याएं हैं, इसलिए \(a_n=2n+3\)। (n=1) पर पहला पद (5) मिलना चाहिए।

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Question 22/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=6n^2-5\) है, तो \(a_4\) क्या होगा?

If \(a_n=6n^2-5\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (91)

Step 1

Concept

(a_4=6(4)2-5=91). First square, then multiply and subtract.

Step 2

Why this answer is correct

The correct answer is B. (91). (a_4=6(4)2-5=91). First square, then multiply and subtract.

Step 3

Exam Tip

(a_4=6(4)2-5=91)। पहले वर्ग करें फिर गुणा और घटाव करें।

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Question 23/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(144,72,36,\ldots\) का (6)वाँ पद क्या है?

What is the (6)th term of the geometric progression \(144,72,36,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{9}{2}\)

Step 1

Concept

The common ratio is \(\frac{1}{2}\), and (a_6=144\left\(\frac{1}{2}\right\)5=\frac{9}{2}). Use powers carefully with a fractional ratio.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{9}{2}\). The common ratio is \(\frac{1}{2}\), and (a_6=144\left\(\frac{1}{2}\right\)5=\frac{9}{2}). Use powers carefully with a fractional ratio.

Step 3

Exam Tip

सार्व अनुपात \(\frac{1}{2}\) है और (a_6=144\left\(\frac{1}{2}\right\)5=\frac{9}{2})। भिन्न अनुपात में घात सावधानी से लगाएं।

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Question 24/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=13n-6\) है, तो \(a_9\) का मान क्या होगा?

If \(a_n=13n-6\), what is the value of \(a_9\)?

Explanation opens after your attempt
Correct Answer

C. (111)

Step 1

Concept

(a_9=13(9)-6=111). Substitute (9) for (n) and simplify.

Step 2

Why this answer is correct

The correct answer is C. (111). (a_9=13(9)-6=111). Substitute (9) for (n) and simplify.

Step 3

Exam Tip

(a_9=13(9)-6=111)। (n) के स्थान पर (9) रखकर सरल करें।

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Question 25/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(28,22,16,10,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(28,22,16,10,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (34-6n)

Step 1

Concept

The first term is (28) and the difference is (-6), so (a_n=28+(n-1)(-6)=34-6n). Pay attention to the sign in a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is A. (34-6n). The first term is (28) and the difference is (-6), so (a_n=28+(n-1)(-6)=34-6n). Pay attention to the sign in a decreasing sequence.

Step 3

Exam Tip

पहला पद (28) और अंतर (-6) है, इसलिए (a_n=28+(n-1)(-6)=34-6n)। घटती श्रेढ़ी में चिह्न पर ध्यान दें।

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Question 26/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

If (a_n=n(n+3)), what is \(a_6\)?

Explanation opens after your attempt
Correct Answer

C. (54)

Step 1

Concept

(a_6=6(9)=54). First find (n+3) inside the bracket.

Step 2

Why this answer is correct

The correct answer is C. (54). (a_6=6(9)=54). First find (n+3) inside the bracket.

Step 3

Exam Tip

(a_6=6(9)=54)। कोष्ठक में (n+3) को पहले निकालें।

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Question 27/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(8,24,72,\ldots\) का (4)वाँ पद क्या है?

What is the (4)th term of the geometric progression \(8,24,72,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (216)

Step 1

Concept

The common ratio is (3), so \(a_4=8\cdot3^3=216\). In a geometric term, the exponent of the ratio is (n-1).

Step 2

Why this answer is correct

The correct answer is C. (216). The common ratio is (3), so \(a_4=8\cdot3^3=216\). In a geometric term, the exponent of the ratio is (n-1).

Step 3

Exam Tip

सार्व अनुपात (3) है, इसलिए \(a_4=8\cdot3^3=216\)। गुणोत्तर पद में अनुपात की घात (n-1) होती है।

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Question 28/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=9n+5\) है, तो \(a_9-a_6\) कितना होगा?

If \(a_n=9n+5\), what is \(a_9-a_6\)?

Explanation opens after your attempt
Correct Answer

C. (27)

Step 1

Concept

\(a_9=86\) and \(a_6=59\), so the difference is (27). Find the terms separately and subtract.

Step 2

Why this answer is correct

The correct answer is C. (27). \(a_9=86\) and \(a_6=59\), so the difference is (27). Find the terms separately and subtract.

Step 3

Exam Tip

\(a_9=86\) और \(a_6=59\), इसलिए अंतर (27) है। पदों को अलग निकालकर घटाएं।

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Question 29/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(9,15,23,33,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(9,15,23,33,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+3n+5\)

Step 1

Concept

Putting \(n^2+3n+5\) gives (9,15,23,33). Check the rule on the first few terms.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+3n+5\). Putting \(n^2+3n+5\) gives (9,15,23,33). Check the rule on the first few terms.

Step 3

Exam Tip

\(n^2+3n+5\) रखने पर (9,15,23,33) मिलते हैं। पहले कुछ पदों पर नियम जांचें।

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Question 30/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=72-8n\) है, तो कौन-सा पद शून्य होगा?

If \(a_n=72-8n\), which term will be zero?

Explanation opens after your attempt
Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

From (72-8n=0), (n=9). For a zero term, set \(a_n\) equal to (0).

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. From (72-8n=0), (n=9). For a zero term, set \(a_n\) equal to (0).

Step 3

Exam Tip

(72-8n=0) से (n=9)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें।

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Question 31/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(4,16,64,256,\ldots\) में (1024) कौन-सा पद है?

In the sequence \(4,16,64,256,\ldots\), which term is (1024)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (4,16,64,256,1024), so (1024) is the fifth term. For small questions, listing terms is quick.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (4,16,64,256,1024), so (1024) is the fifth term. For small questions, listing terms is quick.

Step 3

Exam Tip

पद (4,16,64,256,1024) हैं, इसलिए (1024) पाँचवाँ पद है। छोटे प्रश्नों में पद क्रम से लिखना तेज है।

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Question 32/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि (a_n=\frac{n(n+5)}{2}) है, तो \(a_7\) क्या होगा?

If (a_n=\frac{n(n+5)}{2}), what is \(a_7\)?

Explanation opens after your attempt
Correct Answer

C. (42)

Step 1

Concept

(a_7=\frac{7(12)}{2}=42). Multiply or simplify before dividing.

Step 2

Why this answer is correct

The correct answer is C. (42). (a_7=\frac{7(12)}{2}=42). Multiply or simplify before dividing.

Step 3

Exam Tip

(a_7=\frac{7(12)}{2}=42)। भाग देने से पहले गुणा करें या सरल करें।

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Question 33/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(35,31,27,23,\ldots\) का (10)वाँ पद क्या है?

What is the (10)th term of the sequence \(35,31,27,23,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (-1)

Step 1

Concept

(a_{10}=35+9(-4)=-1). In a decreasing sequence, take the common difference as negative.

Step 2

Why this answer is correct

The correct answer is A. (-1). (a_{10}=35+9(-4)=-1). In a decreasing sequence, take the common difference as negative.

Step 3

Exam Tip

(a_{10}=35+9(-4)=-1)। घटती श्रेढ़ी में समान अंतर ऋणात्मक लें।

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Question 34/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

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

Explanation opens after your attempt
Correct Answer

C. (105)

Step 1

Concept

(a_5=5(5)2-4(5)=105). Square first, then multiply and subtract.

Step 2

Why this answer is correct

The correct answer is C. (105). (a_5=5(5)2-4(5)=105). Square first, then multiply and subtract.

Step 3

Exam Tip

(a_5=5(5)2-4(5)=105)। पहले वर्ग करें फिर गुणा और घटाव करें।

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Question 35/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(4,10,18,28,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(4,10,18,28,\ldots\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Putting \(n^2+3n\) gives (4,10,18,28). Identify both the square and linear parts.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+3n\). Putting \(n^2+3n\) gives (4,10,18,28). Identify both the square and linear parts.

Step 3

Exam Tip

\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। वर्ग और रैखिक भाग दोनों पहचानें।

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Question 36/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=4n+18\) है, तो \(a_n=70\) के लिए (n) क्या होगा?

If \(a_n=4n+18\), what is (n) for \(a_n=70\)?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

From (4n+18=70), (4n=52) and (n=13). Solve the equation to find the position of the term.

Step 2

Why this answer is correct

The correct answer is C. (13). From (4n+18=70), (4n=52) and (n=13). Solve the equation to find the position of the term.

Step 3

Exam Tip

(4n+18=70) से (4n=52) और (n=13)। पद की स्थिति निकालने के लिए समीकरण हल करें।

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Question 37/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(120,40,\frac{40}{3},\ldots\) का (5)वाँ पद क्या है?

What is the (5)th term of the geometric progression \(120,40,\frac{40}{3},\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{40}{27}\)

Step 1

Concept

The common ratio is \(\frac{1}{3}\), and (a_5=120\left\(\frac{1}{3}\right\)4=\frac{40}{27}). Use powers carefully with a fractional ratio.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{40}{27}\). The common ratio is \(\frac{1}{3}\), and (a_5=120\left\(\frac{1}{3}\right\)4=\frac{40}{27}). Use powers carefully with a fractional ratio.

Step 3

Exam Tip

सार्व अनुपात \(\frac{1}{3}\) है और (a_5=120\left\(\frac{1}{3}\right\)4=\frac{40}{27})। भिन्न अनुपात में घात सावधानी से लगाएं।

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Question 38/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=18-6n\) है, तो \(a_5\) क्या होगा?

If \(a_n=18-6n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (-12)

Step 1

Concept

(a_5=18-6(5)=-12). Do not worry if subtraction gives a negative answer.

Step 2

Why this answer is correct

The correct answer is C. (-12). (a_5=18-6(5)=-12). Do not worry if subtraction gives a negative answer.

Step 3

Exam Tip

(a_5=18-6(5)=-12)। घटाव करते समय ऋणात्मक उत्तर से न डरें।

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Question 39/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(7,16,27,40,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(7,16,27,40,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+6n\)

Step 1

Concept

Putting \(n^2+6n\) gives (7,16,27,40). Check the rule on the first four terms.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+6n\). Putting \(n^2+6n\) gives (7,16,27,40). Check the rule on the first four terms.

Step 3

Exam Tip

\(n^2+6n\) रखने पर (7,16,27,40) मिलते हैं। पहले चार पदों पर नियम जांचें।

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Question 40/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=4\cdot5^{n-1}\) है, तो \(a_4\) क्या होगा?

If \(a_n=4\cdot5^{n-1}\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (500)

Step 1

Concept

\(a_4=4\cdot5^3=500\). In a geometric rule, the exponent is (n-1).

Step 2

Why this answer is correct

The correct answer is C. (500). \(a_4=4\cdot5^3=500\). In a geometric rule, the exponent is (n-1).

Step 3

Exam Tip

\(a_4=4\cdot5^3=500\)। गुणोत्तर नियम में घात (n-1) होती है।

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Question 41/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(17,22,27,32,\ldots\) में \(a_n=87\) के लिए (n) क्या है?

In the sequence \(17,22,27,32,\ldots\), what is (n) for \(a_n=87\)?

Explanation opens after your attempt
Correct Answer

C. (15)

Step 1

Concept

(a_n=17+(n-1)5=5n+12), so (5n+12=87) gives (n=15). Set the rule equal to the given term.

Step 2

Why this answer is correct

The correct answer is C. (15). (a_n=17+(n-1)5=5n+12), so (5n+12=87) gives (n=15). Set the rule equal to the given term.

Step 3

Exam Tip

(a_n=17+(n-1)5=5n+12), इसलिए (5n+12=87) से (n=15)। नियम को दिए पद के बराबर रखें।

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Question 42/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

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

Explanation opens after your attempt
Correct Answer

C. (58)

Step 1

Concept

(a_6=62+4(6)-2=58). First square, then add and subtract.

Step 2

Why this answer is correct

The correct answer is C. (58). (a_6=62+4(6)-2=58). First square, then add and subtract.

Step 3

Exam Tip

(a_6=62+4(6)-2=58)। पहले वर्ग करें फिर जोड़ और घटाव करें।

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Question 43/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(3,15,75,\ldots\) में (1875) कौन-सा पद है?

In the geometric progression \(3,15,75,\ldots\), which term is (1875)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (3,15,75,375,1875), so (1875) is the fifth term. Identify the powers in order.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (3,15,75,375,1875), so (1875) is the fifth term. Identify the powers in order.

Step 3

Exam Tip

पद (3,15,75,375,1875) हैं, इसलिए (1875) पाँचवाँ पद है। घातों को क्रम से पहचानें।

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Question 44/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(9,19,29,39,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(9,19,29,39,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (10n-1)

Step 1

Concept

The first term is (9) and the difference is (10), so (a_n=9+(n-1)10=10n-1). Check by putting (n=1).

Step 2

Why this answer is correct

The correct answer is A. (10n-1). The first term is (9) and the difference is (10), so (a_n=9+(n-1)10=10n-1). Check by putting (n=1).

Step 3

Exam Tip

पहला पद (9) और अंतर (10) है, इसलिए (a_n=9+(n-1)10=10n-1)। पहले पद पर (n=1) रखकर जांचें।

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Question 45/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=\frac{7n-2}{3}\) है, तो \(a_5\) क्या होगा?

If \(a_n=\frac{7n-2}{3}\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (11)

Step 1

Concept

(a_5=\frac{7(5)-2}{3}=11). First simplify the numerator and then divide by (3).

Step 2

Why this answer is correct

The correct answer is C. (11). (a_5=\frac{7(5)-2}{3}=11). First simplify the numerator and then divide by (3).

Step 3

Exam Tip

(a_5=\frac{7(5)-2}{3}=11)। पहले अंश को सरल करें फिर (3) से भाग दें।

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Question 46/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(4,16,36,64,\ldots\) का (n)वाँ पद कौन-सा है?

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

Explanation opens after your attempt
Correct Answer

A. \(4n^2\)

Step 1

Concept

The terms are (4(1)2,4(2)2,4(3)2,\ldots), so \(a_n=4n^2\). Identify both the square and the multiplier.

Step 2

Why this answer is correct

The correct answer is A. \(4n^2\). The terms are (4(1)2,4(2)2,4(3)2,\ldots), so \(a_n=4n^2\). Identify both the square and the multiplier.

Step 3

Exam Tip

पद (4(1)2,4(2)2,4(3)2,\ldots) हैं, इसलिए \(a_n=4n^2\)। वर्ग और गुणक दोनों पहचानें।

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Question 47/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

यदि \(a_n=12n+5\) है, तो \(a_7+a_2\) का मान क्या होगा?

If \(a_n=12n+5\), what is the value of \(a_7+a_2\)?

Explanation opens after your attempt
Correct Answer

B. (112)

Step 1

Concept

\(a_7=89\) and \(a_2=29\), so the sum is (118). The correct option should include (118).

Step 2

Why this answer is correct

The correct answer is B. (112). \(a_7=89\) and \(a_2=29\), so the sum is (118). The correct option should include (118).

Step 3

Exam Tip

\(a_7=89\) और \(a_2=29\), इसलिए योग (118) नहीं बल्कि (118) है। सही विकल्पों में (118) होना चाहिए।

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Question 48/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

गुणोत्तर श्रेढ़ी \(9,27,81,\ldots\) में (2187) कौन-सा पद है?

In the geometric progression \(9,27,81,\ldots\), which term is (2187)?

Explanation opens after your attempt
Correct Answer

B. (6)वाँ(6)th

Step 1

Concept

The terms are (9,27,81,243,729,2187), so (2187) is the sixth term. In a geometric progression, multiply by the same ratio each time.

Step 2

Why this answer is correct

The correct answer is B. (6)वाँ / (6)th. The terms are (9,27,81,243,729,2187), so (2187) is the sixth term. In a geometric progression, multiply by the same ratio each time.

Step 3

Exam Tip

पद (9,27,81,243,729,2187) हैं, इसलिए (2187) छठा पद है। गुणोत्तर श्रेढ़ी में हर बार समान अनुपात से गुणा करें।

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Question 49/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

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

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

Explanation opens after your attempt
Correct Answer

B. (138)

Step 1

Concept

(a_6=3(6)2+5(6)=138). Calculate the square first and then add the remaining term.

Step 2

Why this answer is correct

The correct answer is B. (138). (a_6=3(6)2+5(6)=138). Calculate the square first and then add the remaining term.

Step 3

Exam Tip

(a_6=3(6)2+5(6)=138)। वर्ग की गणना पहले करें फिर बाकी पद जोड़ें।

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Question 50/50 Medium Mathematics Sequences and Progressions nth term Class 9 Level 58

अनुक्रम \(50,43,36,29,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(50,43,36,29,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (57-7n)

Step 1

Concept

The first term is (50) and the difference is (-7), so (a_n=50+(n-1)(-7)=57-7n). In a decreasing sequence, take the difference as negative.

Step 2

Why this answer is correct

The correct answer is A. (57-7n). The first term is (50) and the difference is (-7), so (a_n=50+(n-1)(-7)=57-7n). In a decreasing sequence, take the difference as negative.

Step 3

Exam Tip

पहला पद (50) और अंतर (-7) है, इसलिए (a_n=50+(n-1)(-7)=57-7n)। घटती श्रेढ़ी में अंतर को ऋणात्मक लें।

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