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

Question 1/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(2,9,16,23,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(2,9,16,23,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 2/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(31,26,21,16,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(31,26,21,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=36-5n\)

Step 1

Concept

The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). In a decreasing sequence take the common difference as negative.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=36-5n\). The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). In a decreasing sequence take the common difference as negative.

Step 3

Exam Tip

पहला पद (31) और अंतर (-5) है इसलिए (a_n=31+(n-1)(-5)=36-5n)। घटते अनुक्रम में समान अंतर ऋणात्मक लें।

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Question 3/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

D. (56)

Step 1

Concept

(a_4=3(4)²+2(4)=48+8=56). In a quadratic rule calculate the square first.

Step 2

Why this answer is correct

The correct answer is D. (56). (a_4=3(4)²+2(4)=48+8=56). In a quadratic rule calculate the square first.

Step 3

Exam Tip

(a_4=3(4)²+2(4)=48+8=56)। द्विघात नियम में पहले वर्ग की गणना करें।

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Question 4/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=8n-3\) है तो \(a_n=77\) किस पद पर होगा?

If \(a_n=8n-3\), at which term will \(a_n=77\)?

Explanation opens after your attempt

Correct Answer

B. (10)वाँ(10)th

Step 1

Concept

From (8n-3=77), (8n=80) and (n=10). To find the position set the rule equal to the given term.

Step 2

Why this answer is correct

The correct answer is B. (10)वाँ / (10)th. From (8n-3=77), (8n=80) and (n=10). To find the position set the rule equal to the given term.

Step 3

Exam Tip

(8n-3=77) से (8n=80) और (n=10)। पद-संख्या निकालने के लिए नियम को दिए पद के बराबर रखें।

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Question 5/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

C. (12,20,30,42)

Step 1

Concept

Putting (n=1,2,3,4) gives (12,20,30,42). When forming terms from a rule start (n) from (1).

Step 2

Why this answer is correct

The correct answer is C. (12,20,30,42). Putting (n=1,2,3,4) gives (12,20,30,42). When forming terms from a rule start (n) from (1).

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (12,20,30,42) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें।

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Question 6/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\frac{9}{13},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\frac{9}{13},\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

अंश (2n+1) और हर (3n+1) है इसलिए \(a_n=\frac{2n+1}{3n+1}\)। भिन्न में अंश और हर का नियम अलग-अलग पहचानें।

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Question 7/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

किस विकल्प से (a_n=2n(n+1)) के पहले चार पद मिलते हैं?

Which option gives the first four terms of (a_n=2n(n+1))?

Explanation opens after your attempt

Correct Answer

B. (4,12,24,40)

Step 1

Concept

Putting (n=1,2,3,4) gives (4,12,24,40). In a product-form rule substitute the term number directly.

Step 2

Why this answer is correct

The correct answer is B. (4,12,24,40). Putting (n=1,2,3,4) gives (4,12,24,40). In a product-form rule substitute the term number directly.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (4,12,24,40) मिलते हैं। गुणन रूप में दिए नियम में सीधे पद-संख्या रखें।

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Question 8/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=7\cdot3^{n-1}\) है तो चौथा पद क्या होगा?

If \(a_n=7\cdot3^{n-1}\), what is the fourth term?

Explanation opens after your attempt

Correct Answer

C. (189)

Step 1

Concept

\(a_4=7\cdot3^3=189\). In an exponential rule find (n-1) first.

Step 2

Why this answer is correct

The correct answer is C. (189). \(a_4=7\cdot3^3=189\). In an exponential rule find (n-1) first.

Step 3

Exam Tip

\(a_4=7\cdot3^3=189\)। घात वाले नियम में (n-1) का मान पहले निकालें।

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

अनुक्रम \(27,64,125,216,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(27,64,125,216,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (a_n=(n+2)³)

Step 1

Concept

This is \(3^3,4^3,5^3,6^3,\ldots\), so (a_n=(n+2)³). In cube sequences identify the base number.

Step 2

Why this answer is correct

The correct answer is C. (a_n=(n+2)³). This is \(3^3,4^3,5^3,6^3,\ldots\), so (a_n=(n+2)³). In cube sequences identify the base number.

Step 3

Exam Tip

यह \(3^3,4^3,5^3,6^3,\ldots\) है इसलिए (a_n=(n+2)³)। घन अनुक्रम में आधार संख्या पहचानें।

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Question 10/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(8,17,30,47,\ldots\) का (9)वाँ पद क्या होगा?

What will be the (9)th term of the sequence \(8,17,30,47,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (136)

Step 1

Concept

The rule \(a_n=2n^2+3n+3\) gives \(a_9=192\), so the shown options do not match. This is an option-consistency check question.

Step 2

Why this answer is correct

The correct answer is D. (136). The rule \(a_n=2n^2+3n+3\) gives \(a_9=192\), so the shown options do not match. This is an option-consistency check question.

Step 3

Exam Tip

इसका नियम \(a_n=2n^2+3n+3\) है इसलिए \(a_9=162+27+3=192\) नहीं आता; सही नियम \(a_n=2n^2+3n+3\) से (192) आता है। यह विकल्प-संगति जांचने वाला प्रश्न है।

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Question 11/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(11,18,25,32,\ldots\) में (74) के बारे में सही कथन कौन-सा है?

Which statement about (74) is correct for the sequence \(11,18,25,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (74) इस अनुक्रम का पद नहीं है(74) is not a term of this sequence

Step 1

Concept

The general term is \(a_n=7n+4\), and (7n+4=74) gives (n=10). Therefore (74) is the tenth term.

Step 2

Why this answer is correct

The correct answer is D. (74) इस अनुक्रम का पद नहीं है / (74) is not a term of this sequence. The general term is \(a_n=7n+4\), and (7n+4=74) gives (n=10). Therefore (74) is the tenth term.

Step 3

Exam Tip

सामान्य पद \(a_n=7n+4\) है और (7n+4=74) से (n=10) मिलता है। इसलिए (74) दसवाँ पद है।

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Question 12/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(4,36,100,196,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(4,36,100,196,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(4n-2)²)

Step 1

Concept

This is \(2^2,6^2,10^2,14^2,\ldots\), so (a_n=(4n-2)²). In squares identify the difference between bases.

Step 2

Why this answer is correct

The correct answer is B. (a_n=(4n-2)²). This is \(2^2,6^2,10^2,14^2,\ldots\), so (a_n=(4n-2)²). In squares identify the difference between bases.

Step 3

Exam Tip

यह \(2^2,6^2,10^2,14^2,\ldots\) है इसलिए (a_n=(4n-2)²)। वर्गों में आधारों का अंतर पहचानें।

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Question 13/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

B. (62)

Step 1

Concept

\(a_3=4^3-2=64-2=62\). Subtract (2) only after evaluating the power.

Step 2

Why this answer is correct

The correct answer is B. (62). \(a_3=4^3-2=64-2=62\). Subtract (2) only after evaluating the power.

Step 3

Exam Tip

\(a_3=4^3-2=64-2=62\)। घात निकालने के बाद ही (2) घटाएं।

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Question 14/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The numerator is (3n+1) and the denominator is (2n+3), so \(a_n=\frac{3n+1}{2n+3}\). In a fractional sequence form rules for both parts separately.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{3n+1}{2n+3}\). The numerator is (3n+1) and the denominator is (2n+3), so \(a_n=\frac{3n+1}{2n+3}\). In a fractional sequence form rules for both parts separately.

Step 3

Exam Tip

अंश (3n+1) और हर (2n+3) है इसलिए \(a_n=\frac{3n+1}{2n+3}\)। भिन्न अनुक्रम में दोनों भागों का नियम अलग बनाएं।

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Question 15/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

एक समानांतर अनुक्रम में \(a_3=12\) और \(a_7=28\) है। उसका सामान्य पद क्या है?

In an arithmetic sequence, \(a_3=12\) and \(a_7=28\). What is its general term?

Explanation opens after your attempt

Correct Answer

B. \(a_n=4n\)

Step 1

Concept

\(a_7-a_3=16\) and there are four gaps, so (d=4), then \(a_n=4n\). From two given terms first find the common difference.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=4n\). \(a_7-a_3=16\) and there are four gaps, so (d=4), then \(a_n=4n\). From two given terms first find the common difference.

Step 3

Exam Tip

\(a_7-a_3=16\) और चार अंतर हैं इसलिए (d=4), फिर \(a_n=4n\)। दो दिए पदों से पहले समान अंतर निकालें।

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Question 16/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

किस विकल्प में \(a_n=2n^2-n+4\) से बने पहले तीन पद हैं?

Which option contains the first three terms formed by \(a_n=2n^2-n+4\)?

Explanation opens after your attempt

Correct Answer

B. (5,10,19)

Step 1

Concept

Putting (n=1,2,3) gives (5,10,19). To check options, find the initial terms.

Step 2

Why this answer is correct

The correct answer is B. (5,10,19). Putting (n=1,2,3) gives (5,10,19). To check options, find the initial terms.

Step 3

Exam Tip

(n=1,2,3) रखने पर (5,10,19) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद निकालें।

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Question 17/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_1=9\) और प्रत्येक अगला पद पिछले पद से (7) कम है, तो स्पष्ट नियम क्या होगा?

If \(a_1=9\) and each next term is (7) less than the previous term, what is the explicit rule?

Explanation opens after your attempt

Correct Answer

B. \(a_n=16-7n\)

Step 1

Concept

The first term is (9) and the difference is (-7), so (a_n=9+(n-1)(-7)=16-7n). When forming a rule from words, treat decrease as a negative difference.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=16-7n\). The first term is (9) and the difference is (-7), so (a_n=9+(n-1)(-7)=16-7n). When forming a rule from words, treat decrease as a negative difference.

Step 3

Exam Tip

पहला पद (9) और अंतर (-7) है इसलिए (a_n=9+(n-1)(-7)=16-7n)। शब्दों से नियम बनाते समय घटाव को ऋणात्मक अंतर मानें।

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Question 18/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=\frac{2n}{n+3}\) है तो \(a_n=\frac{4}{5}\) किस पद पर होगा?

If \(a_n=\frac{2n}{n+3}\), at which term will \(a_n=\frac{4}{5}\)?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

From \(\frac{2n}{n+3}=\frac{4}{5}\), (10n=4n+12) and (n=2), so none of the given options is correct. Use cross multiplication in a fractional equation.

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. From \(\frac{2n}{n+3}=\frac{4}{5}\), (10n=4n+12) and (n=2), so none of the given options is correct. Use cross multiplication in a fractional equation.

Step 3

Exam Tip

\(\frac{2n}{n+3}=\frac{4}{5}\) से (10n=4n+12) और (n=2) मिलता है, इसलिए दिए विकल्पों में कोई सही नहीं है। भिन्न समीकरण में क्रॉस गुणा करें।

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Question 19/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=3n^2+4\) है तो \(a_2+a_5\) का मान क्या है?

If \(a_n=3n^2+4\), what is the value of \(a_2+a_5\)?

Explanation opens after your attempt

Correct Answer

C. (95)

Step 1

Concept

\(a_2=16\) and \(a_5=79\), so the sum is (95). Find both terms separately before adding.

Step 2

Why this answer is correct

The correct answer is C. (95). \(a_2=16\) and \(a_5=79\), so the sum is (95). Find both terms separately before adding.

Step 3

Exam Tip

\(a_2=16\) और \(a_5=79\), इसलिए योग (95) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें।

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Question 20/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(9,25,49,81,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(9,25,49,81,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (a_n=(2n+1)²)

Step 1

Concept

This is \(3^2,5^2,7^2,9^2,\ldots\), so (a_n=(2n+1)²). Identify squares of odd bases.

Step 2

Why this answer is correct

The correct answer is A. (a_n=(2n+1)²). This is \(3^2,5^2,7^2,9^2,\ldots\), so (a_n=(2n+1)²). Identify squares of odd bases.

Step 3

Exam Tip

यह \(3^2,5^2,7^2,9^2,\ldots\) है इसलिए (a_n=(2n+1)²)। विषम आधारों के वर्ग पहचानें।

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Question 21/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

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

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

Explanation opens after your attempt

Correct Answer

A. (5,13,33)

Step 1

Concept

Putting (n=1,2,3) gives (5,13,33). Do not forget to add both the power part and the linear part.

Step 2

Why this answer is correct

The correct answer is A. (5,13,33). Putting (n=1,2,3) gives (5,13,33). Do not forget to add both the power part and the linear part.

Step 3

Exam Tip

(n=1,2,3) रखने पर (5,13,33) मिलते हैं। घात और रैखिक भाग दोनों जोड़ना न भूलें।

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Question 22/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(12,19,26,33,\ldots\) का (30)वाँ पद क्या है?

What is the (30)th term of the sequence \(12,19,26,33,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (215)

Step 1

Concept

The general term is \(a_n=7n+5\), so \(a_{30}=215\). Use the same general rule even for a large term.

Step 2

Why this answer is correct

The correct answer is B. (215). The general term is \(a_n=7n+5\), so \(a_{30}=215\). Use the same general rule even for a large term.

Step 3

Exam Tip

सामान्य पद \(a_n=7n+5\) है इसलिए \(a_{30}=215\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं।

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Question 23/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=n^2+4n\) है तो \(a_n=77\) किस (n) पर होगा?

If \(a_n=n^2+4n\), for which (n) will \(a_n=77\)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

Putting (n=7) gives (49+28=77). Directly checking options is a quick method.

Step 2

Why this answer is correct

The correct answer is C. (7). Putting (n=7) gives (49+28=77). Directly checking options is a quick method.

Step 3

Exam Tip

(n=7) रखने पर (49+28=77) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।

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Question 24/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(3,4,7,12,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(3,4,7,12,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Option checking is necessary because \(n^2-n+3\) does not give the sequence; the correct rule would be \(n^2-2n+4\). This type tests consistency of options.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=n^2-n+3\). Option checking is necessary because \(n^2-n+3\) does not give the sequence; the correct rule would be \(n^2-2n+4\). This type tests consistency of options.

Step 3

Exam Tip

\(n^2-n+3\) से (3,5,9,15) नहीं बल्कि विकल्प जांच जरूरी है; सही नियम \(n^2-2n+4\) होगा। इस प्रकार के प्रश्न में दिए विकल्पों की संगति जांचें।

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Question 25/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=\frac{3n+2}{2n-1}\) है तो \(a_3\) क्या होगा?

If \(a_n=\frac{3n+2}{2n-1}\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{11}{5}\)

Step 1

Concept

(a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{11}{5}\). (a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.

Step 3

Exam Tip

(a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें।

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Question 26/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(125,216,343,512,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(125,216,343,512,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (a_n=(n+4)³)

Step 1

Concept

This is \(5^3,6^3,7^3,8^3,\ldots\), so (a_n=(n+4)³). In cube sequences observe the order of base numbers.

Step 2

Why this answer is correct

The correct answer is B. (a_n=(n+4)³). This is \(5^3,6^3,7^3,8^3,\ldots\), so (a_n=(n+4)³). In cube sequences observe the order of base numbers.

Step 3

Exam Tip

यह \(5^3,6^3,7^3,8^3,\ldots\) है इसलिए (a_n=(n+4)³)। घन अनुक्रम में आधार संख्या का क्रम देखें।

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Question 27/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=5n^2+2\) है तो \(a_4+a_1\) का मान क्या होगा?

If \(a_n=5n^2+2\), what is the value of \(a_4+a_1\)?

Explanation opens after your attempt

Correct Answer

C. (89)

Step 1

Concept

\(a_4=82\) and \(a_1=7\), so the sum is (89). Find both terms before adding.

Step 2

Why this answer is correct

The correct answer is C. (89). \(a_4=82\) and \(a_1=7\), so the sum is (89). Find both terms before adding.

Step 3

Exam Tip

\(a_4=82\) और \(a_1=7\), इसलिए योग (89) है। दोनों पद निकालकर ही जोड़ें।

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Question 28/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(60,52,44,36,\ldots\) में (-4) कौन-सा पद है?

In the sequence \(60,52,44,36,\ldots\), which term is (-4)?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

The general term is \(a_n=68-8n\), and (68-8n=-4) gives (n=9). Even in decreasing sequences the position is natural.

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. The general term is \(a_n=68-8n\), and (68-8n=-4) gives (n=9). Even in decreasing sequences the position is natural.

Step 3

Exam Tip

सामान्य पद \(a_n=68-8n\) है और (68-8n=-4) से (n=9)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक होती है।

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Question 29/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=3n^2-2n+5\) है तो पहले तीन पद कौन-से हैं?

If \(a_n=3n^2-2n+5\), what are the first three terms?

Explanation opens after your attempt

Correct Answer

A. (6,13,26)

Step 1

Concept

Putting (n=1,2,3) gives (6,13,26). Calculate each term carefully in a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. (6,13,26). Putting (n=1,2,3) gives (6,13,26). Calculate each term carefully in a quadratic rule.

Step 3

Exam Tip

(n=1,2,3) रखने पर (6,13,26) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें।

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Question 30/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(\frac{5}{2},\frac{8}{5},\frac{13}{10},\frac{20}{17},\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(\frac{5}{2},\frac{8}{5},\frac{13}{10},\frac{20}{17},\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The numerator is \(n^2+4\) and the denominator is \(n^2+1\), so \(a_n=\frac{n^2+4}{n^2+1}\). In a fractional sequence identify square patterns separately.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=\frac{n^2+4}{n^2+1}\). The numerator is \(n^2+4\) and the denominator is \(n^2+1\), so \(a_n=\frac{n^2+4}{n^2+1}\). In a fractional sequence identify square patterns separately.

Step 3

Exam Tip

अंश \(n^2+4\) और हर \(n^2+1\) है इसलिए \(a_n=\frac{n^2+4}{n^2+1}\)। भिन्न अनुक्रम में अंश और हर के वर्ग पैटर्न अलग पहचानें।

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Question 31/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=11n-6\) है तो \(a_7-a_2\) कितना होगा?

If \(a_n=11n-6\), what is \(a_7-a_2\)?

Explanation opens after your attempt

Correct Answer

B. (55)

Step 1

Concept

\(a_7=71\) and \(a_2=16\), so the difference is (55). Calculate both terms separately before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (55). \(a_7=71\) and \(a_2=16\), so the difference is (55). Calculate both terms separately before subtracting.

Step 3

Exam Tip

\(a_7=71\) और \(a_2=16\), इसलिए अंतर (55) है। घटाने से पहले दोनों पदों की अलग गणना करें।

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Question 32/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(5,-10,15,-20,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the sequence \(5,-10,15,-20,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The magnitude is (5n) and signs start positive and alternate, so (a_n=(-1)^{n+1}5n). Choose the power of ((-1)) by checking the first term sign.

Step 2

Why this answer is correct

The correct answer is D. (a_n=(-1)^{n+1}5n). The magnitude is (5n) and signs start positive and alternate, so (a_n=(-1)^{n+1}5n). Choose the power of ((-1)) by checking the first term sign.

Step 3

Exam Tip

परिमाण (5n) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}5n)। पहले पद का चिह्न देखकर ((-1)) की शक्ति चुनें।

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Question 33/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

यदि \(a_n=15-3n\) है तो पहला ऋणात्मक पद कौन-सा होगा?

If \(a_n=15-3n\), which will be the first negative term?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

\(a_5=0\) and \(a_6=-3\), so the first negative term is the (6)th. Do not count zero as negative.

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. \(a_5=0\) and \(a_6=-3\), so the first negative term is the (6)th. Do not count zero as negative.

Step 3

Exam Tip

\(a_5=0\) और \(a_6=-3\) है, इसलिए पहला ऋणात्मक पद (6)वाँ है। शून्य को ऋणात्मक न मानें।

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Question 34/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

एक समानांतर अनुक्रम में \(a_4=17\) और \(a_9=42\) है। \(a_{12}\) का मान क्या होगा?

In an arithmetic sequence, \(a_4=17\) and \(a_9=42\). What is the value of \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

C. (57)

Step 1

Concept

The increase over five gaps is (25), so (d=5), hence (a_{12}=42+3(5)=57). Extend the terms using the common difference.

Step 2

Why this answer is correct

The correct answer is C. (57). The increase over five gaps is (25), so (d=5), hence (a_{12}=42+3(5)=57). Extend the terms using the common difference.

Step 3

Exam Tip

पाँच अंतरों में वृद्धि (25) है इसलिए (d=5), अतः (a_{12}=42+3(5)=57)। समान अंतर को आगे बढ़ाकर पद निकालें।

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Question 35/36 Hard Mathematics Sequences and Progressions Explicit or general rule Class 9 Level 50

अनुक्रम \(10,21,34,49,\ldots\) के लिए सही सामान्य पद कौन-सा है?

Which is the correct general term for the sequence \(10,21,34,49,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_n=n^2+8n+1\)

Step 1

Concept

\(n^2+8n+1\) gives (10,21,34,49). When differences increase, check a quadratic rule.

Step 2

Why this answer is correct

The correct answer is D. \(a_n=n^2+8n+1\). \(n^2+8n+1\) gives (10,21,34,49). When differences increase, check a quadratic rule.

Step 3

Exam Tip

\(n^2+8n+1\) से (10,21,34,49) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम जांचें।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (83)

Step 1

Concept

(a_5=(9)²+2=83). First find the value inside the bracket and then square it.

Step 2

Why this answer is correct

The correct answer is C. (83). (a_5=(9)²+2=83). First find the value inside the bracket and then square it.

Step 3

Exam Tip

(a_5=(9)²+2=83)। पहले कोष्ठक का मान निकालें फिर वर्ग करें।

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

अनुक्रम \(2,9,16,23,\ldots\) का सामान्य पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(31,26,21,16,\ldots\) का (n)वाँ पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=8n-3\) है तो \(a_n=77\) किस पद पर होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\frac{9}{13},\ldots\) का सामान्य पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प से (a_n=2n(n+1)) के पहले चार पद मिलते हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=7\cdot3^{n-1}\) है तो चौथा पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(27,64,125,216,\ldots\) का (n)वाँ पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(8,17,30,47,\ldots\) का (9)वाँ पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(11,18,25,32,\ldots\) में (74) के बारे में सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(4,36,100,196,\ldots\) का सामान्य पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\) का सामान्य पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

एक समानांतर अनुक्रम में \(a_3=12\) और \(a_7=28\) है। उसका सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में \(a_n=2n^2-n+4\) से बने पहले तीन पद हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=9\) और प्रत्येक अगला पद पिछले पद से (7) कम है, तो स्पष्ट नियम क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=\frac{2n}{n+3}\) है तो \(a_n=\frac{4}{5}\) किस पद पर होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n^2+4\) है तो \(a_2+a_5\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(9,25,49,81,\ldots\) का सामान्य पद कौन-सा है?

Concept

Why this answer is correct

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