Class 9 Mathematics - Sequences and Progressions - Recursive rule Hard Quiz

Mathematics Sequences and Progressions Recursive rule Hard Class 9 Level 45

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

Level readiness 50/50 Questions
Time Left 25:00 30 sec/question
RewardsCoins + XP
ModeClassic Quiz
Previous Next Level
Share
Question 1 / 50 0 score
Answered 0/50 Correct 0 Time 25:00
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends
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।

Open Question Page
Ask Friends

Mathematics Quiz Navigation

Mathematics Subject

All difficulty level maps

Recursive rule Topic

Topic question list

Sequences and Progressions Chapter

Chapter question list

Search Mathematics

Find related MCQs

All Subjects

Choose another subject
FAQs

Class 9 Mathematics Quiz FAQs

How many questions are in this quiz?

This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.

Is there a timer in this quiz?

Yes, the timer uses 30 seconds per question for Hard difficulty and shows the total remaining time on the page.

Can I open each question separately?

Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.