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

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समांतर श्रेणी \(11,18,25,32,\ldots\) का बारहवाँ पद क्या है?

What is the twelfth term of the arithmetic progression \(11,18,25,32,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (88)

Step 1

Concept

Here (a=11) and (d=7), so \(a_{12}=11+11\times7=88\). In exams, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. (88). Here (a=11) and (d=7), so \(a_{12}=11+11\times7=88\). In exams, use (a_n=a+(n-1)d).

Step 3

Exam Tip

यहाँ (a=11) और (d=7) है, इसलिए \(a_{12}=11+11\times7=88\) है। परीक्षा में (a_n=a+(n-1)d) का प्रयोग करें।

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समांतर श्रेणी \(42,36,30,24,\ldots\) का आठवाँ पद क्या है?

What is the eighth term of the arithmetic progression \(42,36,30,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (0)

Step 1

Concept

Here (d=-6), so (a_8=42+7(-6)=0). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is D. (0). Here (d=-6), so (a_8=42+7(-6)=0). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

यहाँ (d=-6) है, इसलिए (a_8=42+7(-6)=0) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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यदि \(a_n=4n+3\) है, तो (91) कौन-सा पद होगा?

If \(a_n=4n+3\), which term will be (91)?

Explanation opens after your attempt
Correct Answer

C. बाईसवाँ पद(22)nd term

Step 1

Concept

From (4n+3=91), we get (n=22). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is C. बाईसवाँ पद / (22)nd term. From (4n+3=91), we get (n=22). In exams, equate the given term to the general term.

Step 3

Exam Tip

(4n+3=91) से (n=22) मिलता है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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किस समांतर श्रेणी में पहला पद (14) और पंद्रहवाँ पद (84) है, उसका सार्व अंतर क्या है?

In an arithmetic progression whose first term is (14) and fifteenth term is (84), what is the common difference?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

From (84=14+14d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 2

Why this answer is correct

The correct answer is A. (5). From (84=14+14d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 3

Exam Tip

(84=14+14d) से (d=5) है। परीक्षा में (n)वें पद में (n-1) का ध्यान रखें।

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समांतर श्रेणी \(7,12,17,22,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(7,12,17,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(a_n=5n+2\)

Step 1

Concept

The first term is (7) and the difference is (5), so \(a_n=5n+2\). In exams, check the first term by putting (n=1).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=5n+2\). The first term is (7) and the difference is (5), so \(a_n=5n+2\). In exams, check the first term by putting (n=1).

Step 3

Exam Tip

पहला पद (7) और अंतर (5) है, इसलिए \(a_n=5n+2\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।

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समांतर श्रेणी \(2,5,8,11,\ldots\) के पहले (10) पदों का योग क्या है?

What is the sum of the first (10) terms of the arithmetic progression \(2,5,8,11,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (155)

Step 1

Concept

\(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\). In exams, use the formula for \(S_n\).

Step 2

Why this answer is correct

The correct answer is D. (155). \(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\). In exams, use the formula for \(S_n\).

Step 3

Exam Tip

\(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\) है। परीक्षा में योग के लिए \(S_n\) का सूत्र लगाएँ।

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समांतर श्रेणी \(3,8,13,18,\ldots\) के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of the arithmetic progression \(3,8,13,18,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (164)

Step 1

Concept

\(S_8=\frac{8}{2}[2\times3+7\times5]=164\). In exams, calculate inside the bracket first.

Step 2

Why this answer is correct

The correct answer is C. (164). \(S_8=\frac{8}{2}[2\times3+7\times5]=164\). In exams, calculate inside the bracket first.

Step 3

Exam Tip

\(S_8=\frac{8}{2}[2\times3+7\times5]=164\) है। परीक्षा में कोष्ठक के अंदर की गणना पहले करें।

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यदि \(a_3=17\) और (d=4) है, तो पहला पद (a) क्या होगा?

If \(a_3=17\) and (d=4), what is the first term (a)?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

\(a_3=a+2d\), so (17=a+8) and (a=9). In exams, subtract two differences from the third term.

Step 2

Why this answer is correct

The correct answer is B. (9). \(a_3=a+2d\), so (17=a+8) and (a=9). In exams, subtract two differences from the third term.

Step 3

Exam Tip

\(a_3=a+2d\), इसलिए (17=a+8) और (a=9) है। परीक्षा में तीसरे पद से दो अंतर घटाएँ।

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समांतर श्रेणी \(25,21,17,13,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(25,21,17,13,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(a_n=29-4n\)

Step 1

Concept

The rule \(a_n=29-4n\) gives (25) at (n=1) and (21) at (n=2). In exams, match the first term in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=29-4n\). The rule \(a_n=29-4n\) gives (25) at (n=1) and (21) at (n=2). In exams, match the first term in a decreasing progression.

Step 3

Exam Tip

(n=1) पर (25) और (n=2) पर (21) देने वाला नियम \(a_n=29-4n\) है। परीक्षा में घटती श्रेणी में पहला पद मिलाएँ।

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समांतर श्रेणी \(4,10,16,22,\ldots\) में (70) कौन-सा पद है?

In the arithmetic progression \(4,10,16,22,\ldots\), which term is (70)?

Explanation opens after your attempt
Correct Answer

C. बारहवाँ पद(12)th term

Step 1

Concept

From (4+(n-1)6=70), we get (n=12). In exams, form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is C. बारहवाँ पद / (12)th term. From (4+(n-1)6=70), we get (n=12). In exams, form an equation to find the term number.

Step 3

Exam Tip

(4+(n-1)6=70) से (n=12) मिलता है। परीक्षा में पद संख्या के लिए समीकरण बनाएँ।

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यदि समांतर श्रेणी के पहले पाँच पदों का योग (95) है और (a=7) है, तो (d) क्या है?

If the sum of the first five terms of an arithmetic progression is (95) and (a=7), what is (d)?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

From \(\frac{5}{2}[14+4d]=95\), (d=6). In exams, keep (n-1) correct in the sum formula.

Step 2

Why this answer is correct

The correct answer is B. (6). From \(\frac{5}{2}[14+4d]=95\), (d=6). In exams, keep (n-1) correct in the sum formula.

Step 3

Exam Tip

\(\frac{5}{2}[14+4d]=95\) से (d=6) मिलता है। परीक्षा में योग सूत्र में (n-1) सही रखें।

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समांतर श्रेणी \(1,4,7,10,\ldots\) के पहले (20) पदों का योग क्या है?

What is the sum of the first (20) terms of the arithmetic progression \(1,4,7,10,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (590)

Step 1

Concept

\(S_{20}=\frac{20}{2}[2+19\times3]=590\). In exams, add (19d) for (20) terms.

Step 2

Why this answer is correct

The correct answer is C. (590). \(S_{20}=\frac{20}{2}[2+19\times3]=590\). In exams, add (19d) for (20) terms.

Step 3

Exam Tip

\(S_{20}=\frac{20}{2}[2+19\times3]=590\) है। परीक्षा में (20) पदों के लिए (19d) जोड़ें।

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यदि \(a_n=9n-2\) है, तो पहले (6) पदों का योग क्या होगा?

If \(a_n=9n-2\), what is the sum of the first (6) terms?

Explanation opens after your attempt
Correct Answer

B. (186)

Step 1

Concept

The first six terms are (7,16,25,34,43,52), and their sum is (186). In exams, you can verify the sum by listing terms from the rule.

Step 2

Why this answer is correct

The correct answer is B. (186). The first six terms are (7,16,25,34,43,52), and their sum is (186). In exams, you can verify the sum by listing terms from the rule.

Step 3

Exam Tip

पहले छह पद (7,16,25,34,43,52) हैं और योग (186) है। परीक्षा में नियम से पद निकालकर भी योग जाँच सकते हैं।

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समांतर श्रेणी \(17,24,31,\ldots\) का वह पद कौन-सा है जो (80) है?

Which term of the arithmetic progression \(17,24,31,\ldots\) is (80)?

Explanation opens after your attempt
Correct Answer

C. दसवाँ पद(10)th term

Step 1

Concept

From (17+(n-1)7=80), we get (n=10). In exams, equate the given term to (a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. दसवाँ पद / (10)th term. From (17+(n-1)7=80), we get (n=10). In exams, equate the given term to (a+(n-1)d).

Step 3

Exam Tip

(17+(n-1)7=80) से (n=10) मिलता है। परीक्षा में दिए पद को (a+(n-1)d) के बराबर रखें।

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यदि \(a_2=12\) और \(a_6=32\) है, तो पहला पद क्या होगा?

If \(a_2=12\) and \(a_6=32\), what is the first term?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

From (4d=20), (d=5), and from (a+d=12), (a=7). In exams, find (d) first and then (a).

Step 2

Why this answer is correct

The correct answer is C. (7). From (4d=20), (d=5), and from (a+d=12), (a=7). In exams, find (d) first and then (a).

Step 3

Exam Tip

(4d=20) से (d=5) और (a+d=12) से (a=7) है। परीक्षा में पहले (d) निकालें फिर (a) निकालें।

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समांतर श्रेणी \(30,27,24,21,\ldots\) में शून्य कौन-सा पद है?

In the arithmetic progression \(30,27,24,21,\ldots\), which term is zero?

Explanation opens after your attempt
Correct Answer

C. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (30+(n-1)(-3)=0), (n=11). In exams, form and solve an equation for the zero term.

Step 2

Why this answer is correct

The correct answer is C. ग्यारहवाँ पद / (11)th term. From (30+(n-1)(-3)=0), (n=11). In exams, form and solve an equation for the zero term.

Step 3

Exam Tip

(30+(n-1)(-3)=0) से (n=11) है। परीक्षा में शून्य पद के लिए समीकरण बनाकर हल करें।

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समांतर श्रेणी \(9,16,23,\ldots\) के पहले (12) पदों का योग क्या है?

What is the sum of the first (12) terms of the arithmetic progression \(9,16,23,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (570)

Step 1

Concept

\(S_{12}=\frac{12}{2}[18+11\times7]=570\). In exams, add (2a+(n-1)d) correctly.

Step 2

Why this answer is correct

The correct answer is C. (570). \(S_{12}=\frac{12}{2}[18+11\times7]=570\). In exams, add (2a+(n-1)d) correctly.

Step 3

Exam Tip

\(S_{12}=\frac{12}{2}[18+11\times7]=570\) है। परीक्षा में (2a+(n-1)d) को सही जोड़ें।

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यदि समांतर श्रेणी \(x,,x+6,,x+12,\ldots\) में तीसरा पद (25) है, तो (x) क्या है?

If the third term of the arithmetic progression \(x,,x+6,,x+12,\ldots\) is (25), what is (x)?

Explanation opens after your attempt
Correct Answer

B. (13)

Step 1

Concept

The third term is (x+12=25), so (x=13). In exams, put algebraic terms directly into an equation.

Step 2

Why this answer is correct

The correct answer is B. (13). The third term is (x+12=25), so (x=13). In exams, put algebraic terms directly into an equation.

Step 3

Exam Tip

तीसरा पद (x+12=25) है, इसलिए (x=13) है। परीक्षा में बीजीय पदों को सीधे समीकरण में रखें।

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समांतर श्रेणी \(5,9,13,\ldots\) में (41) तक कितने पद हैं?

How many terms are there up to (41) in the arithmetic progression \(5,9,13,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (10)

Step 1

Concept

From (5+(n-1)4=41), (n=10). In exams, equate the last term to the general term.

Step 2

Why this answer is correct

The correct answer is C. (10). From (5+(n-1)4=41), (n=10). In exams, equate the last term to the general term.

Step 3

Exam Tip

(5+(n-1)4=41) से (n=10) है। परीक्षा में अंतिम पद को सामान्य पद के बराबर रखें।

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यदि किसी समांतर श्रेणी के पहले (4) पद (3,8,13,18) हैं, तो \(S_4\) क्या है?

If the first (4) terms of an arithmetic progression are (3,8,13,18), what is \(S_4\)?

Explanation opens after your attempt
Correct Answer

B. (42)

Step 1

Concept

The sum is (3+8+13+18=42). In exams, direct addition is also fast for small (n).

Step 2

Why this answer is correct

The correct answer is B. (42). The sum is (3+8+13+18=42). In exams, direct addition is also fast for small (n).

Step 3

Exam Tip

योग (3+8+13+18=42) है। परीक्षा में छोटे (n) के लिए सीधे जोड़ना भी तेज होता है।

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समांतर श्रेणी \(12,18,24,\ldots\) का कौन-सा पद (96) है?

Which term of the arithmetic progression \(12,18,24,\ldots\) is (96)?

Explanation opens after your attempt
Correct Answer

C. पंद्रहवाँ पद(15)th term

Step 1

Concept

From (12+(n-1)6=96), (n=15). In exams, isolate (n-1) while solving.

Step 2

Why this answer is correct

The correct answer is C. पंद्रहवाँ पद / (15)th term. From (12+(n-1)6=96), (n=15). In exams, isolate (n-1) while solving.

Step 3

Exam Tip

(12+(n-1)6=96) से (n=15) है। परीक्षा में (n-1) को अलग करके हल करें।

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समांतर श्रेणी \(2,7,12,17,\ldots\) के पहले (15) पदों का योग क्या है?

What is the sum of the first (15) terms of the arithmetic progression \(2,7,12,17,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (555)

Step 1

Concept

\(S_{15}=\frac{15}{2}[4+14\times5]=555\). In exams, simplify the bracket first when a fraction appears.

Step 2

Why this answer is correct

The correct answer is B. (555). \(S_{15}=\frac{15}{2}[4+14\times5]=555\). In exams, simplify the bracket first when a fraction appears.

Step 3

Exam Tip

\(S_{15}=\frac{15}{2}[4+14\times5]=555\) है। परीक्षा में भिन्न आए तो पहले कोष्ठक सरल करें।

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समांतर श्रेणी \(100,92,84,\ldots\) में (20) कौन-सा पद है?

In the arithmetic progression \(100,92,84,\ldots\), which term is (20)?

Explanation opens after your attempt
Correct Answer

B. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (100+(n-1)(-8)=20), (n=11). In exams, use the negative difference for a decreasing term.

Step 2

Why this answer is correct

The correct answer is B. ग्यारहवाँ पद / (11)th term. From (100+(n-1)(-8)=20), (n=11). In exams, use the negative difference for a decreasing term.

Step 3

Exam Tip

(100+(n-1)(-8)=20) से (n=11) है। परीक्षा में घटते पद के लिए ऋणात्मक अंतर लगाएँ।

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यदि \(a_n=50-3n\) है, तो कौन-सा पद (5) के बराबर होगा?

If \(a_n=50-3n\), which term will be equal to (5)?

Explanation opens after your attempt
Correct Answer

C. पंद्रहवाँ पद(15)th term

Step 1

Concept

From (50-3n=5), (n=15). In exams, keep signs correct in a decreasing linear rule.

Step 2

Why this answer is correct

The correct answer is C. पंद्रहवाँ पद / (15)th term. From (50-3n=5), (n=15). In exams, keep signs correct in a decreasing linear rule.

Step 3

Exam Tip

(50-3n=5) से (n=15) है। परीक्षा में घटते रैखिक नियम में चिह्न सही रखें।

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समांतर श्रेणी \(7,14,21,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of the arithmetic progression \(7,14,21,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (315)

Step 1

Concept

This is the sum of the first (9) multiples of (7), which is (315). In exams, identify sequences of multiples quickly.

Step 2

Why this answer is correct

The correct answer is B. (315). This is the sum of the first (9) multiples of (7), which is (315). In exams, identify sequences of multiples quickly.

Step 3

Exam Tip

यह (7) के पहले (9) गुणजों का योग है, जो (315) है। परीक्षा में गुणजों की श्रेणी को जल्दी पहचानें।

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यदि (a=18) और (d=-2) है, तो पहले (7) पदों का योग क्या है?

If (a=18) and (d=-2), what is the sum of the first (7) terms?

Explanation opens after your attempt
Correct Answer

B. (84)

Step 1

Concept

(S_7=\frac{7}{2}[36+6(-2)]=84). In exams, put negative (d) inside brackets.

Step 2

Why this answer is correct

The correct answer is B. (84). (S_7=\frac{7}{2}[36+6(-2)]=84). In exams, put negative (d) inside brackets.

Step 3

Exam Tip

(S_7=\frac{7}{2}[36+6(-2)]=84) है। परीक्षा में ऋणात्मक (d) को कोष्ठक में रखें।

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समांतर श्रेणी \(8,12,16,\ldots\) के पहले (25) पदों का योग क्या है?

What is the sum of the first (25) terms of the arithmetic progression \(8,12,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (1400)

Step 1

Concept

\(S_{25}=\frac{25}{2}[16+24\times4]=1400\). In exams, take ((n-1)=24) for (n=25).

Step 2

Why this answer is correct

The correct answer is C. (1400). \(S_{25}=\frac{25}{2}[16+24\times4]=1400\). In exams, take ((n-1)=24) for (n=25).

Step 3

Exam Tip

\(S_{25}=\frac{25}{2}[16+24\times4]=1400\) है। परीक्षा में (n=25) के लिए ((n-1)=24) लें।

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समांतर श्रेणी \(13,10,7,4,\ldots\) में (-8) कौन-सा पद है?

In the arithmetic progression \(13,10,7,4,\ldots\), which term is (-8)?

Explanation opens after your attempt
Correct Answer

A. आठवाँ पद(8)th term

Step 1

Concept

From (13+(n-1)(-3)=-8), (n=8). In exams, use the same formula even for negative terms.

Step 2

Why this answer is correct

The correct answer is A. आठवाँ पद / (8)th term. From (13+(n-1)(-3)=-8), (n=8). In exams, use the same formula even for negative terms.

Step 3

Exam Tip

(13+(n-1)(-3)=-8) से (n=8) है। परीक्षा में ऋणात्मक पदों के लिए भी वही सूत्र लगाएँ।

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समांतर श्रेणी \(6,11,16,\ldots\) में कितने पदों तक योग (451) होगा?

How many terms of the arithmetic progression \(6,11,16,\ldots\) have sum (451)?

Explanation opens after your attempt
Correct Answer

B. (11)

Step 1

Concept

In (S_n=\frac{n}{2}[12+5(n-1)]), putting (n=11) gives (451). In exams, you can also check quickly by substituting options.

Step 2

Why this answer is correct

The correct answer is B. (11). In (S_n=\frac{n}{2}[12+5(n-1)]), putting (n=11) gives (451). In exams, you can also check quickly by substituting options.

Step 3

Exam Tip

(S_n=\frac{n}{2}[12+5(n-1)]) में (n=11) रखने पर (451) मिलता है। परीक्षा में विकल्पों को रखकर भी जल्दी जाँच सकते हैं।

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