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alternating-index MCQ Questions for Class 9

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8 questions tagged with alternating-index.

Question 1/8 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=7\) और (a_{n+1}=2a_n+(-1)^n n) है तो \(a_5\) क्या होगा?

If \(a_1=7\) and (a_{n+1}=2a_n+(-1)^n n), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (110)

Step 1

Concept

The terms are (7,13,28,53,110), so \(a_5=110\). Exam tip: the sign of ((-1)^n) changes with even and odd (n).

Step 2

Why this answer is correct

The correct answer is C. (110). The terms are (7,13,28,53,110), so \(a_5=110\). Exam tip: the sign of ((-1)^n) changes with even and odd (n).

Step 3

Exam Tip

पद (7,13,28,53,110) हैं इसलिए \(a_5=110\) है। ((-1)^n) का चिह्न सम-विषम (n) से बदलता है।

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Question 2/8 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=10\) और (a_{n+1}=a_n+(-1)^{n+1}(n+2)) है तो \(a_5\) क्या होगा?

If \(a_1=10\) and (a_{n+1}=a_n+(-1)^{n+1}(n+2)), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. (8)

Step 1

Concept

The terms are (10,13,9,14,8), so \(a_5=8\). Exam tip: check the sign at each step in alternating rules.

Step 2

Why this answer is correct

The correct answer is B. (8). The terms are (10,13,9,14,8), so \(a_5=8\). Exam tip: check the sign at each step in alternating rules.

Step 3

Exam Tip

पद (10,13,9,14,8) हैं इसलिए \(a_5=8\) है। चिह्न बदलने वाले नियम में हर चरण का संकेत देखें।

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Question 3/8 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=6\) और (a_{n+1}=a_n+(-1)^n(2n)) है तो \(a_4\) क्या होगा?

If \(a_1=6\) and (a_{n+1}=a_n+(-1)^n(2n)), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

The terms are (6,4,8,2), so \(a_4=2\). Exam tip: the sign of ((-1)^n) changes at each step.

Step 2

Why this answer is correct

The correct answer is A. (2). The terms are (6,4,8,2), so \(a_4=2\). Exam tip: the sign of ((-1)^n) changes at each step.

Step 3

Exam Tip

पद (6,4,8,2) हैं इसलिए \(a_4=2\) है। ((-1)^n) का चिह्न हर चरण में बदलता है।

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Question 4/8 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=6\) और (a_{n+1}=a_n+(-1)^n(2n)) है तो \(a_5\) क्या होगा?

If \(a_1=6\) and (a_{n+1}=a_n+(-1)^n(2n)), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

The terms are (6,4,8,2,10), so \(a_5=10\). Exam tip: check even and odd (n) in sign-changing rules.

Step 2

Why this answer is correct

The correct answer is C. (6). The terms are (6,4,8,2,10), so \(a_5=10\). Exam tip: check even and odd (n) in sign-changing rules.

Step 3

Exam Tip

पद (6,4,8,2,10) नहीं बल्कि \(a_5=10\) है। चिह्न बदलने वाले पदों में सम-विषम (n) जाँचें।

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Question 5/8 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=8\) और (a_{n+1}=a_n+2(-1)^n+n) है तो \(a_3\) क्या होगा?

If \(a_1=8\) and (a_{n+1}=a_n+2(-1)^n+n), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (11)

Step 1

Concept

\(a_2=8-2+1=7\) and \(a_3=7+2+2=11\). Exam tip: the sign of ((-1)^n) changes at each step.

Step 2

Why this answer is correct

The correct answer is C. (11). \(a_2=8-2+1=7\) and \(a_3=7+2+2=11\). Exam tip: the sign of ((-1)^n) changes at each step.

Step 3

Exam Tip

\(a_2=8-2+1=7\) और \(a_3=7+2+2=11\) है। ((-1)^n) का चिह्न हर चरण में बदलता है।

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Question 6/8 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=8\) और (a_{n+1}=a_n+2(-1)^n+n) है तो \(a_4\) क्या होगा?

If \(a_1=8\) and (a_{n+1}=a_n+2(-1)^n+n), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (11)

Step 1

Concept

The terms are (8,7,11,12), so \(a_4=12\). Exam tip: track both the alternating sign part and (n).

Step 2

Why this answer is correct

The correct answer is B. (11). The terms are (8,7,11,12), so \(a_4=12\). Exam tip: track both the alternating sign part and (n).

Step 3

Exam Tip

पद (8,7,11,12) हैं इसलिए \(a_4=12\) है। चिह्न बदलने वाले भाग और (n) दोनों देखें।

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Question 7/8 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और (a_{n+1}=a_n+(-1)^{n+1}n) है तो \(a_4\) क्या होगा?

If \(a_1=5\) and (a_{n+1}=a_n+(-1)^{n+1}n), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

D. (7)

Step 1

Concept

The terms are (5,6,4,7), so \(a_4=7\). Exam tip: check the sign of ((-1)^{n+1}) at each step.

Step 2

Why this answer is correct

The correct answer is D. (7). The terms are (5,6,4,7), so \(a_4=7\). Exam tip: check the sign of ((-1)^{n+1}) at each step.

Step 3

Exam Tip

पद (5,6,4,7) हैं इसलिए \(a_4=7\) है। ((-1)^{n+1}) के चिह्न को हर चरण में जाँचें।

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Question 8/8 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और (a_{n+1}=a_n+(-1)^{n+1}n) है तो \(a_5\) क्या होगा?

If \(a_1=5\) and (a_{n+1}=a_n+(-1)^{n+1}n), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

The terms are (5,6,4,7,3), so \(a_5=3\). The correct option should include (3).

Step 2

Why this answer is correct

The correct answer is C. (7). The terms are (5,6,4,7,3), so \(a_5=3\). The correct option should include (3).

Step 3

Exam Tip

पद (5,6,4,7,3) नहीं बल्कि \(a_5=3\) है। सही विकल्प में (3) होना चाहिए।

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