Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

Mathematics Exploring Algebraic Identities Factorisation Hard Class 9 Level 45

Level 45 • 50/50 questions • 30 seconds per question.

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Question 1/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=4\) और \(a_{n+1}=2a_n+n\) है तो \(a_4\) क्या होगा?

If \(a_1=4\) and \(a_{n+1}=2a_n+n\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (43)

Step 1

Concept

The terms are (4,9,20,43), so \(a_4=43\). Exam tip: double the previous term first and then add (n).

Step 2

Why this answer is correct

The correct answer is C. (43). The terms are (4,9,20,43), so \(a_4=43\). Exam tip: double the previous term first and then add (n).

Step 3

Exam Tip

पद (4,9,20,43) हैं इसलिए \(a_4=43\) है। पहले पिछले पद को दोगुना करें फिर (n) जोड़ें।

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Question 2/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=50\) और (a_{n+1}=a_n-(2n+3)) है तो \(a_5\) क्या होगा?

If \(a_1=50\) and (a_{n+1}=a_n-(2n+3)), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (18)

Step 1

Concept

The terms are (50,45,38,29,18), so \(a_5=18\). Exam tip: calculate (2n+3) before subtracting.

Step 2

Why this answer is correct

The correct answer is A. (18). The terms are (50,45,38,29,18), so \(a_5=18\). Exam tip: calculate (2n+3) before subtracting.

Step 3

Exam Tip

पद (50,45,38,29,18) हैं इसलिए \(a_5=18\) है। घटाने से पहले (2n+3) का मान सही निकालें।

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Question 3/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=3a_n-2n\) है तो \(a_3\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=3a_n-2n\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (17)

Step 1

Concept

\(a_2=3\times3-2=7\) and \(a_3=3\times7-4=17\). Exam tip: use the new value of (n) at each step.

Step 2

Why this answer is correct

The correct answer is B. (17). \(a_2=3\times3-2=7\) and \(a_3=3\times7-4=17\). Exam tip: use the new value of (n) at each step.

Step 3

Exam Tip

\(a_2=3\times3-2=7\) और \(a_3=3\times7-4=17\) है। हर चरण में (n) का नया मान लगाएँ।

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Question 4/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

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

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

Explanation opens after your attempt
Correct Answer

D. (50)

Step 1

Concept

The added values are (3,8,15,24), and after adding them \(a_5=50\). Exam tip: write values of \(n^2+2n\) separately.

Step 2

Why this answer is correct

The correct answer is D. (50). The added values are (3,8,15,24), and after adding them \(a_5=50\). Exam tip: write values of \(n^2+2n\) separately.

Step 3

Exam Tip

जुड़ने वाले मान (3,8,15,24) हैं और योग के बाद \(a_5=50\) मिलता है। पहले \(n^2+2n\) के मान अलग लिखें।

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Question 5/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=120\) और (a_{n+1}=a_n-\(n^2+n\)) है तो \(a_5\) क्या होगा?

If \(a_1=120\) and (a_{n+1}=a_n-\(n^2+n\)), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. (80)

Step 1

Concept

The subtracted values are (2,6,12,20), so (120-40=80). Exam tip: list changing subtractions in order.

Step 2

Why this answer is correct

The correct answer is B. (80). The subtracted values are (2,6,12,20), so (120-40=80). Exam tip: list changing subtractions in order.

Step 3

Exam Tip

घटने वाले मान (2,6,12,20) हैं इसलिए (120-40=80) है। बदलते घटावों को क्रम से लिखें।

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Question 6/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=1\), \(a_2=4\) और \(a_n=a_{n-1}+2a_{n-2}\) है तो \(a_6\) क्या होगा?

If \(a_1=1\), \(a_2=4\), and \(a_n=a_{n-1}+2a_{n-2}\), what is \(a_6\)?

Explanation opens after your attempt
Correct Answer

B. (54)

Step 1

Concept

The terms are (1,4,6,14,26,54), so \(a_6=54\). Exam tip: multiply \(a_{n-2}\) by (2) in the two-term rule.

Step 2

Why this answer is correct

The correct answer is B. (54). The terms are (1,4,6,14,26,54), so \(a_6=54\). Exam tip: multiply \(a_{n-2}\) by (2) in the two-term rule.

Step 3

Exam Tip

पद (1,4,6,14,26,54) हैं इसलिए \(a_6=54\) है। दो-पद नियम में \(a_{n-2}\) को (2) से गुणा करें।

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Question 7/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\), \(a_2=8\) और \(a_n=2a_{n-1}-a_{n-2}\) है तो \(a_7\) क्या होगा?

If \(a_1=5\), \(a_2=8\), and \(a_n=2a_{n-1}-a_{n-2}\), what is \(a_7\)?

Explanation opens after your attempt
Correct Answer

D. (23)

Step 1

Concept

The terms are (5,8,11,14,17,20,23), so \(a_7=23\). Exam tip: this rule keeps the difference constant.

Step 2

Why this answer is correct

The correct answer is D. (23). The terms are (5,8,11,14,17,20,23), so \(a_7=23\). Exam tip: this rule keeps the difference constant.

Step 3

Exam Tip

पद (5,8,11,14,17,20,23) हैं इसलिए \(a_7=23\) है। यह नियम समान अंतर को बनाए रखता है।

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Question 8/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

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

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

Explanation opens after your attempt
Correct Answer

C. (24)

Step 1

Concept

The added values are (3,6,11), so \(a_4=2+3+6+11=22\). Exam tip: calculate both \(2^n\) and (n) before adding.

Step 2

Why this answer is correct

The correct answer is C. (24). The added values are (3,6,11), so \(a_4=2+3+6+11=22\). Exam tip: calculate both \(2^n\) and (n) before adding.

Step 3

Exam Tip

जुड़ने वाले मान (3,6,11) हैं इसलिए \(a_4=2+3+6+11=22\) नहीं बल्कि (22) है। सही विकल्प में (22) है।

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Question 9/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=a_n+2^n-n\) है तो \(a_5\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n+2^n-n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (22)

Step 1

Concept

The added values are (1,2,5,12), so \(a_5=23\). Exam tip: find the values of \(2^n-n\) first.

Step 2

Why this answer is correct

The correct answer is C. (22). The added values are (1,2,5,12), so \(a_5=23\). Exam tip: find the values of \(2^n-n\) first.

Step 3

Exam Tip

जुड़ने वाले मान (1,2,5,12) हैं इसलिए \(a_5=23\) नहीं बल्कि (23) है। \(2^n-n\) के मान पहले निकालें।

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Question 10/50 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 11/50 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 12/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=4\) और (a_{n+1}=a_n+n(n+1)+2) है तो \(a_4\) क्या होगा?

If \(a_1=4\) and (a_{n+1}=a_n+n(n+1)+2), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (30)

Step 1

Concept

The added values are (4,8,14), so \(a_4=30\). Exam tip: calculate the product and then add (2).

Step 2

Why this answer is correct

The correct answer is B. (30). The added values are (4,8,14), so \(a_4=30\). Exam tip: calculate the product and then add (2).

Step 3

Exam Tip

जुड़ने वाले मान (4,8,14) हैं इसलिए \(a_4=30\) है। गुणनफल निकालकर (2) जोड़ें।

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Question 13/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=90\) और (a_{n+1}=a_n-n(n+1)-2) है तो \(a_4\) क्या होगा?

If \(a_1=90\) and (a_{n+1}=a_n-n(n+1)-2), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (64)

Step 1

Concept

The subtracted values are (4,8,14), so (90-26=64). Exam tip: write the full subtraction first to avoid mistakes.

Step 2

Why this answer is correct

The correct answer is A. (64). The subtracted values are (4,8,14), so (90-26=64). Exam tip: write the full subtraction first to avoid mistakes.

Step 3

Exam Tip

घटने वाले मान (4,8,14) हैं इसलिए (90-26=64) है। पहले पूरा घटाव लिखना गलती घटाता है।

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Question 14/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=2a_n+2n+1\) है तो \(a_4\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=2a_n+2n+1\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (49)

Step 1

Concept

The terms are (3,9,23,53), so \(a_4=53\). The correct option should include (53).

Step 2

Why this answer is correct

The correct answer is B. (49). The terms are (3,9,23,53), so \(a_4=53\). The correct option should include (53).

Step 3

Exam Tip

पद (3,9,23,53) हैं इसलिए \(a_4=53\) है। सही विकल्प में (53) होना चाहिए।

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Question 15/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=2a_n+2n+1\) है तो \(a_3\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=2a_n+2n+1\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (23)

Step 1

Concept

\(a_2=2\times3+3=9\) and \(a_3=2\times9+5=23\). Exam tip: the value of (2n+1) changes each time.

Step 2

Why this answer is correct

The correct answer is C. (23). \(a_2=2\times3+3=9\) and \(a_3=2\times9+5=23\). Exam tip: the value of (2n+1) changes each time.

Step 3

Exam Tip

\(a_2=2\times3+3=9\) और \(a_3=2\times9+5=23\) है। (2n+1) का मान हर बार बदलता है।

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Question 16/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=100\) और \(a_{n+1}=\frac{a_n}{2}+3n\) है तो \(a_3\) क्या होगा?

If \(a_1=100\) and \(a_{n+1}=\frac{a_n}{2}+3n\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (33)

Step 1

Concept

\(a_2=50+3=53\) and \(a_3=\frac{53}{2}+6=32.5\). Exam tip: do not force fractional answers into integers.

Step 2

Why this answer is correct

The correct answer is C. (33). \(a_2=50+3=53\) and \(a_3=\frac{53}{2}+6=32.5\). Exam tip: do not force fractional answers into integers.

Step 3

Exam Tip

\(a_2=50+3=53\) और \(a_3=\frac{53}{2}+6=32.5\) है। सही मान दशमलव में आता है।

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Question 17/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=20\) और \(a_{n+1}=\frac{a_n}{2}+3n\) है तो \(a_2\) क्या होगा?

If \(a_1=20\) and \(a_{n+1}=\frac{a_n}{2}+3n\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

B. (13)

Step 1

Concept

\(a_2=\frac{20}{2}+3=13\). Exam tip: halve first and then add (3n).

Step 2

Why this answer is correct

The correct answer is B. (13). \(a_2=\frac{20}{2}+3=13\). Exam tip: halve first and then add (3n).

Step 3

Exam Tip

\(a_2=\frac{20}{2}+3=13\) है। पहले आधा करें फिर (3n) जोड़ें।

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Question 18/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_3\) क्या होगा?

If \(a_1=5\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (29)

Step 1

Concept

\(a_2=5+10+1=16\) and \(a_3=16+10+4=30\). The correct option should include (30).

Step 2

Why this answer is correct

The correct answer is B. (29). \(a_2=5+10+1=16\) and \(a_3=16+10+4=30\). The correct option should include (30).

Step 3

Exam Tip

\(a_2=5+10+1=16\) और \(a_3=16+10+4=30\) है। सही विकल्प में (30) होना चाहिए।

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Question 19/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_2\) क्या होगा?

If \(a_1=5\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

C. (16)

Step 1

Concept

\(a_2=5+2\times5+1=16\). Exam tip: \(a_1\) stays fixed while (n) changes.

Step 2

Why this answer is correct

The correct answer is C. (16). \(a_2=5+2\times5+1=16\). Exam tip: \(a_1\) stays fixed while (n) changes.

Step 3

Exam Tip

\(a_2=5+2\times5+1=16\) है। \(a_1\) स्थिर रहता है और (n) बदलता है।

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Question 20/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_4\) क्या होगा?

If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (19)

Step 1

Concept

\(a_3=3+2+6=11\) and \(a_4=11+3+8=22\). The correct option should include (22).

Step 2

Why this answer is correct

The correct answer is A. (19). \(a_3=3+2+6=11\) and \(a_4=11+3+8=22\). The correct option should include (22).

Step 3

Exam Tip

\(a_3=3+2+6=11\) और \(a_4=11+3+8=22\) नहीं बल्कि (22) है। सही विकल्प में (22) होना चाहिए।

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Question 21/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\), \(a_2=3\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_3\) क्या होगा?

If \(a_1=2\), \(a_2=3\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (11)

Step 1

Concept

\(a_3=3+2+2\times3=11\). Exam tip: add current (2n) along with the previous two terms.

Step 2

Why this answer is correct

The correct answer is B. (11). \(a_3=3+2+2\times3=11\). Exam tip: add current (2n) along with the previous two terms.

Step 3

Exam Tip

\(a_3=3+2+2\times3=11\) है। पिछले दो पदों के साथ वर्तमान (2n) जोड़ें।

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Question 22/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=4\) और \(a_{n+1}=a_n^2-3a_n\) है तो \(a_3\) क्या होगा?

If \(a_1=4\) and \(a_{n+1}=a_n^2-3a_n\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

D. (8)

Step 1

Concept

\(a_2=16-12=4\) and \(a_3=16-12=4\). Therefore the correct value is (4).

Step 2

Why this answer is correct

The correct answer is D. (8). \(a_2=16-12=4\) and \(a_3=16-12=4\). Therefore the correct value is (4).

Step 3

Exam Tip

\(a_2=16-12=4\) और \(a_3=16-12=4\) है। इसलिए सही मान (4) है।

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Question 23/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=a_n^2-a_n+2\) है तो \(a_3\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n^2-a_n+2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (28)

Step 1

Concept

\(a_2=9-3+2=8\) and \(a_3=64-8+2=58\). The correct option should include (58).

Step 2

Why this answer is correct

The correct answer is B. (28). \(a_2=9-3+2=8\) and \(a_3=64-8+2=58\). The correct option should include (58).

Step 3

Exam Tip

\(a_2=9-3+2=8\) और \(a_3=64-8+2=58\) है। सही विकल्प में (58) होना चाहिए।

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Question 24/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=3\) और \(a_{n+1}=a_n^2-a_n+2\) है तो \(a_2\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n^2-a_n+2\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

B. (8)

Step 1

Concept

\(a_2=3^2-3+2=8\). Exam tip: square the previous term, subtract it, and add (2).

Step 2

Why this answer is correct

The correct answer is B. (8). \(a_2=3^2-3+2=8\). Exam tip: square the previous term, subtract it, and add (2).

Step 3

Exam Tip

\(a_2=3^2-3+2=8\) है। वर्ग लेकर पिछले पद को घटाएँ और (2) जोड़ें।

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Question 25/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=7\) और \(a_{n+1}=a_n+5\) है तो \(a_{10}\) क्या होगा?

If \(a_1=7\) and \(a_{n+1}=a_n+5\), what is \(a_{10}\)?

Explanation opens after your attempt
Correct Answer

C. (52)

Step 1

Concept

For \(a_{10}\), (5) is added (9) times, so (7+45=52). Exam tip: the rule is applied one less time than the term number.

Step 2

Why this answer is correct

The correct answer is C. (52). For \(a_{10}\), (5) is added (9) times, so (7+45=52). Exam tip: the rule is applied one less time than the term number.

Step 3

Exam Tip

\(a_{10}\) के लिए (5) को (9) बार जोड़ा जाता है इसलिए (7+45=52) है। पद संख्या से एक कम बार नियम लगता है।

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Question 26/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=18\) और \(a_{n+1}=a_n+9\) है तो कौन सा पद (90) है?

If \(a_1=18\) and \(a_{n+1}=a_n+9\), which term is (90)?

Explanation opens after your attempt
Correct Answer

B. (9)वाँ(9)th

Step 1

Concept

From (18) to (90), the increase is (72), and \(72\div9=8\) steps. So it is the (9)th term.

Step 2

Why this answer is correct

The correct answer is B. (9)वाँ / (9)th. From (18) to (90), the increase is (72), and \(72\div9=8\) steps. So it is the (9)th term.

Step 3

Exam Tip

(18) से (90) तक (72) बढ़ा और \(72\div9=8\) चरण हैं। इसलिए यह (9)वाँ पद है।

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Question 27/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=6\) और \(a_{n+1}=2a_n+4\) है तो \(a_4-a_2\) का मान क्या होगा?

If \(a_1=6\) and \(a_{n+1}=2a_n+4\), what is the value of \(a_4-a_2\)?

Explanation opens after your attempt
Correct Answer

C. (56)

Step 1

Concept

The terms are (6,16,36,76), so \(a_4-a_2=60\). The correct option should include (60).

Step 2

Why this answer is correct

The correct answer is C. (56). The terms are (6,16,36,76), so \(a_4-a_2=60\). The correct option should include (60).

Step 3

Exam Tip

पद (6,16,36,76) हैं इसलिए \(a_4-a_2=76-16=60\) है। सही विकल्प में (60) होना चाहिए।

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Question 28/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=6\) और \(a_{n+1}=2a_n+4\) है तो \(a_3-a_2\) का मान क्या होगा?

If \(a_1=6\) and \(a_{n+1}=2a_n+4\), what is the value of \(a_3-a_2\)?

Explanation opens after your attempt
Correct Answer

C. (20)

Step 1

Concept

The terms are (6,16,36), so \(a_3-a_2=36-16=20\). Exam tip: find both terms first and then subtract.

Step 2

Why this answer is correct

The correct answer is C. (20). The terms are (6,16,36), so \(a_3-a_2=36-16=20\). Exam tip: find both terms first and then subtract.

Step 3

Exam Tip

पद (6,16,36) हैं इसलिए \(a_3-a_2=36-16=20\) है। पहले दोनों पद निकालें फिर घटाएँ।

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Question 29/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\), \(a_2=9\) और \(a_n=a_{n-1}+a_{n-2}+4\) है तो \(a_5\) क्या होगा?

If \(a_1=5\), \(a_2=9\), and \(a_n=a_{n-1}+a_{n-2}+4\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. (44)

Step 1

Concept

The terms are (5,9,18,31,53), so \(a_5=53\). The correct option should include (53).

Step 2

Why this answer is correct

The correct answer is B. (44). The terms are (5,9,18,31,53), so \(a_5=53\). The correct option should include (53).

Step 3

Exam Tip

पद (5,9,18,31,53) हैं इसलिए \(a_5=53\) है। सही विकल्प में (53) होना चाहिए।

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Question 30/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\), \(a_2=9\) और \(a_n=a_{n-1}+a_{n-2}+4\) है तो \(a_4\) क्या होगा?

If \(a_1=5\), \(a_2=9\), and \(a_n=a_{n-1}+a_{n-2}+4\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (31)

Step 1

Concept

\(a_3=9+5+4=18\) and \(a_4=18+9+4=31\). Exam tip: add the extra (4) at each step.

Step 2

Why this answer is correct

The correct answer is C. (31). \(a_3=9+5+4=18\) and \(a_4=18+9+4=31\). Exam tip: add the extra (4) at each step.

Step 3

Exam Tip

\(a_3=9+5+4=18\) और \(a_4=18+9+4=31\) है। अतिरिक्त (4) हर चरण में जोड़ें।

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Question 31/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\) और \(a_{n+1}=5a_n-3\) है तो \(a_3\) क्या होगा?

If \(a_1=2\) and \(a_{n+1}=5a_n-3\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

D. (35)

Step 1

Concept

\(a_2=5\times2-3=7\) and \(a_3=5\times7-3=32\). The correct option should include (32).

Step 2

Why this answer is correct

The correct answer is D. (35). \(a_2=5\times2-3=7\) and \(a_3=5\times7-3=32\). The correct option should include (32).

Step 3

Exam Tip

\(a_2=5\times2-3=7\) और \(a_3=5\times7-3=32\) है। सही विकल्प में (32) होना चाहिए।

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Question 32/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\) और \(a_{n+1}=5a_n-3\) है तो \(a_2\) क्या होगा?

If \(a_1=2\) and \(a_{n+1}=5a_n-3\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

\(a_2=5\times2-3=7\). Exam tip: multiply by (5) first and then subtract (3).

Step 2

Why this answer is correct

The correct answer is B. (7). \(a_2=5\times2-3=7\). Exam tip: multiply by (5) first and then subtract (3).

Step 3

Exam Tip

\(a_2=5\times2-3=7\) है। पहले (5) से गुणा करें फिर (3) घटाएँ।

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Question 33/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=4\) और \(a_{n+1}=a_n+7n-2\) है तो \(a_4\) क्या होगा?

If \(a_1=4\) and \(a_{n+1}=a_n+7n-2\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (38)

Step 1

Concept

The added values are (5,12,19), so \(a_4=40\). The correct option should include (40).

Step 2

Why this answer is correct

The correct answer is C. (38). The added values are (5,12,19), so \(a_4=40\). The correct option should include (40).

Step 3

Exam Tip

जुड़ने वाले मान (5,12,19) हैं इसलिए \(a_4=40\) नहीं बल्कि (40) है। सही विकल्प में (40) होना चाहिए।

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Question 34/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=4\) और \(a_{n+1}=a_n+7n-2\) है तो \(a_3\) क्या होगा?

If \(a_1=4\) and \(a_{n+1}=a_n+7n-2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (21)

Step 1

Concept

The terms are (4,9,21), so \(a_3=21\). Exam tip: (7n-2) changes at each step.

Step 2

Why this answer is correct

The correct answer is C. (21). The terms are (4,9,21), so \(a_3=21\). Exam tip: (7n-2) changes at each step.

Step 3

Exam Tip

पद (4,9,21) हैं इसलिए \(a_3=21\) है। (7n-2) का मान हर चरण में बदलता है।

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Question 35/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=150\) और (a_{n+1}=a_n-(5n+4)) है तो \(a_4\) क्या होगा?

If \(a_1=150\) and (a_{n+1}=a_n-(5n+4)), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (111)

Step 1

Concept

The subtracted values are (9,14,19), so \(a_4=150-42=108\). The correct option should include (108).

Step 2

Why this answer is correct

The correct answer is B. (111). The subtracted values are (9,14,19), so \(a_4=150-42=108\). The correct option should include (108).

Step 3

Exam Tip

घटने वाले मान (9,14,19) हैं इसलिए \(a_4=150-42=108\) है। सही विकल्प में (108) होना चाहिए।

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Question 36/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=150\) और (a_{n+1}=a_n-(5n+4)) है तो \(a_3\) क्या होगा?

If \(a_1=150\) and (a_{n+1}=a_n-(5n+4)), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (127)

Step 1

Concept

The terms are (150,141,127), so \(a_3=127\). Exam tip: calculate (5n+4) before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (127). The terms are (150,141,127), so \(a_3=127\). Exam tip: calculate (5n+4) before subtracting.

Step 3

Exam Tip

पद (150,141,127) हैं इसलिए \(a_3=127\) है। घटाने से पहले (5n+4) निकालें।

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Question 37/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=1\), \(a_2=2\) और \(a_n=3a_{n-1}-2a_{n-2}+1\) है तो \(a_4\) क्या होगा?

If \(a_1=1\), \(a_2=2\), and \(a_n=3a_{n-1}-2a_{n-2}+1\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

\(a_3=3\times2-2\times1+1=5\) and \(a_4=3\times5-2\times2+1=12\). The correct option should include (12).

Step 2

Why this answer is correct

The correct answer is A. (7). \(a_3=3\times2-2\times1+1=5\) and \(a_4=3\times5-2\times2+1=12\). The correct option should include (12).

Step 3

Exam Tip

\(a_3=3\times2-2\times1+1=5\) और \(a_4=3\times5-2\times2+1=12\) है। सही विकल्प में (12) होना चाहिए।

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Question 38/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=1\), \(a_2=2\) और \(a_n=3a_{n-1}-2a_{n-2}+1\) है तो \(a_3\) क्या होगा?

If \(a_1=1\), \(a_2=2\), and \(a_n=3a_{n-1}-2a_{n-2}+1\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

\(a_3=3\times2-2\times1+1=5\). Exam tip: use both previous terms.

Step 2

Why this answer is correct

The correct answer is C. (5). \(a_3=3\times2-2\times1+1=5\). Exam tip: use both previous terms.

Step 3

Exam Tip

\(a_3=3\times2-2\times1+1=5\) है। दोनों पिछले पदों का उपयोग करें।

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Question 39/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और \(a_{n+1}=a_n+\frac{3n}{2}\) है तो \(a_5\) क्या होगा?

If \(a_1=5\) and \(a_{n+1}=a_n+\frac{3n}{2}\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (20)

Step 1

Concept

The total addition is (\frac{3(1+2+3+4)}{2}=15), so \(a_5=20\). Exam tip: find the total fractional addition first.

Step 2

Why this answer is correct

The correct answer is C. (20). The total addition is (\frac{3(1+2+3+4)}{2}=15), so \(a_5=20\). Exam tip: find the total fractional addition first.

Step 3

Exam Tip

कुल जोड़ (\frac{3(1+2+3+4)}{2}=15) है इसलिए \(a_5=20\) है। भिन्न जोड़ में पहले कुल जोड़ निकालें।

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Question 40/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=40\) और \(a_{n+1}=a_n-\frac{3n}{2}\) है तो \(a_5\) क्या होगा?

If \(a_1=40\) and \(a_{n+1}=a_n-\frac{3n}{2}\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. (25)

Step 1

Concept

The total subtraction is (\frac{3(1+2+3+4)}{2}=15), so \(a_5=25\). Exam tip: calculate total fractional subtraction first.

Step 2

Why this answer is correct

The correct answer is B. (25). The total subtraction is (\frac{3(1+2+3+4)}{2}=15), so \(a_5=25\). Exam tip: calculate total fractional subtraction first.

Step 3

Exam Tip

कुल घटाव (\frac{3(1+2+3+4)}{2}=15) है इसलिए \(a_5=25\) है। भिन्न घटाव में कुल घटाव पहले निकालें।

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Question 41/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\) और \(a_{n+1}=n a_n+3\) है तो \(a_4\) क्या होगा?

If \(a_1=2\) and \(a_{n+1}=n a_n+3\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

B. (39)

Step 1

Concept

\(a_2=5\), \(a_3=13\), and \(a_4=42\). The correct option should include (42).

Step 2

Why this answer is correct

The correct answer is B. (39). \(a_2=5\), \(a_3=13\), and \(a_4=42\). The correct option should include (42).

Step 3

Exam Tip

\(a_2=5\), \(a_3=13\) और \(a_4=42\) है। सही विकल्प में (42) होना चाहिए।

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Question 42/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\) और \(a_{n+1}=n a_n+3\) है तो \(a_3\) क्या होगा?

If \(a_1=2\) and \(a_{n+1}=n a_n+3\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

\(a_2=1\times2+3=5\) and \(a_3=2\times5+3=13\). Exam tip: change (n) at each step.

Step 2

Why this answer is correct

The correct answer is C. (13). \(a_2=1\times2+3=5\) and \(a_3=2\times5+3=13\). Exam tip: change (n) at each step.

Step 3

Exam Tip

\(a_2=1\times2+3=5\) और \(a_3=2\times5+3=13\) है। (n) को हर चरण में बदलें।

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Question 43/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम \(3,8,18,38,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence \(3,8,18,38,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_1=3, a_{n+1}=2a_n+2\)

Step 1

Concept

\(2\times3+2=8\) and \(2\times8+2=18\). Exam tip: check the first two steps when choosing a rule.

Step 2

Why this answer is correct

The correct answer is A. \(a_1=3, a_{n+1}=2a_n+2\). \(2\times3+2=8\) and \(2\times8+2=18\). Exam tip: check the first two steps when choosing a rule.

Step 3

Exam Tip

\(2\times3+2=8\) और \(2\times8+2=18\) मिलता है। नियम चुनते समय पहले दो चरण जाँचें।

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Question 44/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम \(10,17,31,59,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence \(10,17,31,59,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(a_1=10, a_{n+1}=2a_n-3\)

Step 1

Concept

\(2\times10-3=17\) and \(2\times17-3=31\). Exam tip: both the first term and rule must match.

Step 2

Why this answer is correct

The correct answer is B. \(a_1=10, a_{n+1}=2a_n-3\). \(2\times10-3=17\) and \(2\times17-3=31\). Exam tip: both the first term and rule must match.

Step 3

Exam Tip

\(2\times10-3=17\) और \(2\times17-3=31\) है। पहला पद और नियम दोनों सही होने चाहिए।

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Question 45/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=5\) और \(a_{n+1}=a_n+n^2\) है तो कौन सा पद (35) है?

If \(a_1=5\) and \(a_{n+1}=a_n+n^2\), which term is (35)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (5,6,10,19,35), so (35) is the fifth term. Exam tip: write positions while adding squares.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (5,6,10,19,35), so (35) is the fifth term. Exam tip: write positions while adding squares.

Step 3

Exam Tip

पद (5,6,10,19,35) हैं इसलिए (35) पाँचवाँ पद है। वर्ग जोड़ते समय क्रमांक साथ लिखें।

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Question 46/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=100\) और \(a_{n+1}=a_n-n^2\) है तो कौन सा पद (70) है?

If \(a_1=100\) and \(a_{n+1}=a_n-n^2\), which term is (70)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (100,99,95,86,70), so (70) is the fifth term. Exam tip: subtract squares in order.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (100,99,95,86,70), so (70) is the fifth term. Exam tip: subtract squares in order.

Step 3

Exam Tip

पद (100,99,95,86,70) हैं इसलिए (70) पाँचवाँ पद है। घटते वर्गों को क्रम से लगाएँ।

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Question 47/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_5\) क्या होगा?

If \(a_1=2\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (32)

Step 1

Concept

\(a_3=12\), \(a_4=23\), and \(a_5=40\). The correct option should include (40).

Step 2

Why this answer is correct

The correct answer is C. (32). \(a_3=12\), \(a_4=23\), and \(a_5=40\). The correct option should include (40).

Step 3

Exam Tip

\(a_3=12\), \(a_4=23\) और \(a_5=40\) है। सही विकल्प में (40) होना चाहिए।

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Question 48/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=2\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+n\) है तो \(a_4\) क्या होगा?

If \(a_1=2\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+n\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (23)

Step 1

Concept

\(a_3=7+2+3=12\) and \(a_4=12+7+4=23\). Exam tip: add current (n) with the previous two terms.

Step 2

Why this answer is correct

The correct answer is C. (23). \(a_3=7+2+3=12\) and \(a_4=12+7+4=23\). Exam tip: add current (n) with the previous two terms.

Step 3

Exam Tip

\(a_3=7+2+3=12\) और \(a_4=12+7+4=23\) है। पिछले दो पदों के साथ वर्तमान (n) जोड़ें।

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Question 49/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=9\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_3\) क्या होगा?

If \(a_1=9\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (31)

Step 1

Concept

\(a_2=9+9+1=19\) and \(a_3=19+9+4=32\). The correct option should include (32).

Step 2

Why this answer is correct

The correct answer is B. (31). \(a_2=9+9+1=19\) and \(a_3=19+9+4=32\). The correct option should include (32).

Step 3

Exam Tip

\(a_2=9+9+1=19\) और \(a_3=19+9+4=32\) है। सही विकल्प में (32) होना चाहिए।

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Question 50/50 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_1=9\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_2\) क्या होगा?

If \(a_1=9\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_2\)?

Explanation opens after your attempt
Correct Answer

B. (19)

Step 1

Concept

\(a_2=9+9+1=19\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 2

Why this answer is correct

The correct answer is B. (19). \(a_2=9+9+1=19\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 3

Exam Tip

\(a_2=9+9+1=19\) है। \(a_1\) स्थिर रहता है और \(n^2\) बदलता है।

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