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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

C. (33)

Step 1

Concept

The terms are (5,9,15,23,33), so \(a_5=33\). Exam tip: the value of (2n+2) changes at each step.

Step 2

Why this answer is correct

The correct answer is C. (33). The terms are (5,9,15,23,33), so \(a_5=33\). Exam tip: the value of (2n+2) changes at each step.

Step 3

Exam Tip

पद (5,9,15,23,33) हैं इसलिए \(a_5=33\) है। (2n+2) का मान हर चरण में बदलता है।

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Question 2/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=60\) और (a_{n+1}=a_n-(3n+1)) है तो \(a_4\) क्या होगा?

If \(a_1=60\) and (a_{n+1}=a_n-(3n+1)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (39)

Step 1

Concept

The terms are (60,56,49,39), so \(a_4=39\). Exam tip: calculate (3n+1) correctly before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (39). The terms are (60,56,49,39), so \(a_4=39\). Exam tip: calculate (3n+1) correctly before subtracting.

Step 3

Exam Tip

पद (60,56,49,39) हैं इसलिए \(a_4=39\) है। घटाने से पहले (3n+1) सही निकालें।

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Question 3/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

C. (43)

Step 1

Concept

The terms are (3,8,20,43), so \(a_4=43\). Exam tip: double the previous term first and then add (n+1).

Step 2

Why this answer is correct

The correct answer is C. (43). The terms are (3,8,20,43), so \(a_4=43\). Exam tip: double the previous term first and then add (n+1).

Step 3

Exam Tip

पद (3,8,20,43) हैं इसलिए \(a_4=43\) है। पहले पिछले पद को दोगुना करें फिर (n+1) जोड़ें।

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Question 4/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=7\) और \(a_{n+1}=3a_n-2n\) है तो \(a_3\) क्या होगा?

If \(a_1=7\) and \(a_{n+1}=3a_n-2n\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

D. (57)

Step 1

Concept

\(a_2=3\times7-2=19\) and \(a_3=3\times19-4=53\). Exam tip: when (n=2), subtract (4).

Step 2

Why this answer is correct

The correct answer is D. (57). \(a_2=3\times7-2=19\) and \(a_3=3\times19-4=53\). Exam tip: when (n=2), subtract (4).

Step 3

Exam Tip

\(a_2=3\times7-2=19\) और \(a_3=3\times19-4=53\) नहीं बल्कि \(a_3=53\) है। सही गणना में (n=2) पर (4) घटता है।

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Question 5/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=7\) और \(a_{n+1}=3a_n-2n\) है तो \(a_2\) क्या होगा?

If \(a_1=7\) and \(a_{n+1}=3a_n-2n\), what is \(a_2\)?

Explanation opens after your attempt

Correct Answer

B. (19)

Step 1

Concept

\(a_2=3\times7-2\times1=19\). Exam tip: use (n=1) for the next term.

Step 2

Why this answer is correct

The correct answer is B. (19). \(a_2=3\times7-2\times1=19\). Exam tip: use (n=1) for the next term.

Step 3

Exam Tip

\(a_2=3\times7-2\times1=19\) है। अगले पद के लिए (n=1) रखें।

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Question 6/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (27)

Step 1

Concept

The terms give \(a_3=9\), \(a_4=19\), and \(a_5=37\). Exam tip: multiply \(a_{n-2}\) by (2) before adding.

Step 2

Why this answer is correct

The correct answer is B. (27). The terms give \(a_3=9\), \(a_4=19\), and \(a_5=37\). Exam tip: multiply \(a_{n-2}\) by (2) before adding.

Step 3

Exam Tip

पद (2,5,9,19,37) नहीं हैं क्योंकि \(a_5=19+2\times9=37\) होगा। इसलिए सही मान (37) है।

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Question 7/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (19)

Step 1

Concept

\(a_3=5+2\times2=9\) and \(a_4=9+2\times5=19\). Exam tip: write positions while using two-term rules.

Step 2

Why this answer is correct

The correct answer is B. (19). \(a_3=5+2\times2=9\) and \(a_4=9+2\times5=19\). Exam tip: write positions while using two-term rules.

Step 3

Exam Tip

\(a_3=5+2\times2=9\) और \(a_4=9+2\times5=19\) है। दो-पद नियम में क्रमांक साथ लिखें।

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Question 8/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=4\), \(a_2=10\) और \(a_n=2a_{n-1}-a_{n-2}\) है तो \(a_6\) क्या होगा?

If \(a_1=4\), \(a_2=10\), and \(a_n=2a_{n-1}-a_{n-2}\), what is \(a_6\)?

Explanation opens after your attempt

Correct Answer

D. (34)

Step 1

Concept

The terms are (4,10,16,22,28,34), so \(a_6=34\). Exam tip: this rule preserves a constant difference.

Step 2

Why this answer is correct

The correct answer is D. (34). The terms are (4,10,16,22,28,34), so \(a_6=34\). Exam tip: this rule preserves a constant difference.

Step 3

Exam Tip

पद (4,10,16,22,28,34) हैं इसलिए \(a_6=34\) है। यह नियम समान अंतर बनाए रखता है।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (32)

Step 1

Concept

The terms are (6,9,17,32), so \(a_4=32\). Exam tip: calculate the new value of \(n^2+2n\) each time.

Step 2

Why this answer is correct

The correct answer is C. (32). The terms are (6,9,17,32), so \(a_4=32\). Exam tip: calculate the new value of \(n^2+2n\) each time.

Step 3

Exam Tip

पद (6,9,17,32) हैं इसलिए \(a_4=32\) है। \(n^2+2n\) का मान हर बार नया निकालें।

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Question 10/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (70)

Step 1

Concept

The terms are (90,88,82,70), so \(a_4=70\). Exam tip: subtract (2,6,12) in order.

Step 2

Why this answer is correct

The correct answer is B. (70). The terms are (90,88,82,70), so \(a_4=70\). Exam tip: subtract (2,6,12) in order.

Step 3

Exam Tip

पद (90,88,82,70) हैं इसलिए \(a_4=70\) है। \(n^2+n\) के मान (2,6,12) क्रम से घटाएँ।

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Question 11/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

D. (40)

Step 1

Concept

The terms are (1,4,13,40), so \(a_4=40\). Exam tip: add (3,9,27), the values of \(3^n\).

Step 2

Why this answer is correct

The correct answer is D. (40). The terms are (1,4,13,40), so \(a_4=40\). Exam tip: add (3,9,27), the values of \(3^n\).

Step 3

Exam Tip

पद (1,4,13,40) हैं इसलिए \(a_4=40\) है। \(3^n\) के मान (3,9,27) जोड़ें।

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Question 12/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=100\) और \(a_{n+1}=a_n-3^n\) है तो \(a_4\) क्या होगा?

If \(a_1=100\) and \(a_{n+1}=a_n-3^n\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (61)

Step 1

Concept

The terms are (100,97,88,61), so \(a_4=61\). Exam tip: subtract (3,9,27) in order.

Step 2

Why this answer is correct

The correct answer is A. (61). The terms are (100,97,88,61), so \(a_4=61\). Exam tip: subtract (3,9,27) in order.

Step 3

Exam Tip

पद (100,97,88,61) हैं इसलिए \(a_4=61\) है। (3,9,27) को क्रम से घटाएँ।

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Question 13/50 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 14/50 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 15/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

D. (39)

Step 1

Concept

The terms are (3,7,17,35), so \(a_4=35\). Exam tip: add (4,10,18), the values of (n(n+3)).

Step 2

Why this answer is correct

The correct answer is D. (39). The terms are (3,7,17,35), so \(a_4=35\). Exam tip: add (4,10,18), the values of (n(n+3)).

Step 3

Exam Tip

पद (3,7,17,35) नहीं बल्कि \(a_4=35\) है। (n(n+3)) के मान (4,10,18) जोड़ें।

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Question 16/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (17)

Step 1

Concept

The terms are (3,7,17), so \(a_3=17\). Exam tip: calculate the product before adding.

Step 2

Why this answer is correct

The correct answer is B. (17). The terms are (3,7,17), so \(a_3=17\). Exam tip: calculate the product before adding.

Step 3

Exam Tip

पद (3,7,17) हैं इसलिए \(a_3=17\) है। गुणनफल निकालकर जोड़ें।

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Question 17/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=120\) और (a_{n+1}=a_n-n(n+3)) है तो \(a_4\) क्या होगा?

If \(a_1=120\) and (a_{n+1}=a_n-n(n+3)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (88)

Step 1

Concept

The terms are (120,116,106,88), so \(a_4=88\). Exam tip: subtract (4,10,18) in order.

Step 2

Why this answer is correct

The correct answer is A. (88). The terms are (120,116,106,88), so \(a_4=88\). Exam tip: subtract (4,10,18) in order.

Step 3

Exam Tip

पद (120,116,106,88) हैं इसलिए \(a_4=88\) है। (4,10,18) को क्रम से घटाएँ।

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Question 18/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

A. (61)

Step 1

Concept

The terms are (4,13,31,67), so \(a_4=67\). The correct option should include (67).

Step 2

Why this answer is correct

The correct answer is A. (61). The terms are (4,13,31,67), so \(a_4=67\). The correct option should include (67).

Step 3

Exam Tip

पद (4,13,31,67) नहीं बल्कि \(a_4=67\) है। सही विकल्प में (67) होना चाहिए।

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Question 19/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=4\) और \(a_{n+1}=2a_n+5\) है तो \(a_3\) क्या होगा?

If \(a_1=4\) and \(a_{n+1}=2a_n+5\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

The terms are (4,13,31), so \(a_3=31\). Exam tip: double first and then add (5).

Step 2

Why this answer is correct

The correct answer is C. (31). The terms are (4,13,31), so \(a_3=31\). Exam tip: double first and then add (5).

Step 3

Exam Tip

पद (4,13,31) हैं इसलिए \(a_3=31\) है। पहले दोगुना करें फिर (5) जोड़ें।

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Question 20/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

\(a_2=3\times5+1+2=18\). Exam tip: use (n=1) for the next term.

Step 2

Why this answer is correct

The correct answer is B. (18). \(a_2=3\times5+1+2=18\). Exam tip: use (n=1) for the next term.

Step 3

Exam Tip

\(a_2=3\times5+1+2=18\) है। अगले पद के लिए (n=1) रखें।

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Question 21/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

C. (58)

Step 1

Concept

\(a_2=18\) and \(a_3=3\times18+2+2=58\). Exam tip: do not forget to change (n).

Step 2

Why this answer is correct

The correct answer is C. (58). \(a_2=18\) and \(a_3=3\times18+2+2=58\). Exam tip: do not forget to change (n).

Step 3

Exam Tip

\(a_2=18\) और \(a_3=3\times18+2+2=58\) है। (n) का मान बदलना न भूलें।

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Question 22/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

C. (28)

Step 1

Concept

The terms are (2,4,8,15,26), so \(a_5=26\). Exam tip: add the increasing increments carefully.

Step 2

Why this answer is correct

The correct answer is C. (28). The terms are (2,4,8,15,26), so \(a_5=26\). Exam tip: add the increasing increments carefully.

Step 3

Exam Tip

पद (2,4,8,15,26) नहीं बल्कि \(a_5=26\) है। (2,4,7,11) जैसे बढ़ते जोड़ ध्यान से जोड़ें।

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Question 23/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

The terms are (2,4,8,15), so \(a_4=15\). Exam tip: the increment is a triangular number plus (1).

Step 2

Why this answer is correct

The correct answer is B. (15). The terms are (2,4,8,15), so \(a_4=15\). Exam tip: the increment is a triangular number plus (1).

Step 3

Exam Tip

पद (2,4,8,15) हैं इसलिए \(a_4=15\) है। त्रिभुजीय संख्या में (1) जोड़कर अगला जोड़ बनता है।

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Question 24/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=80\) और (a_{n+1}=a_n-\frac{n(n+1)}{2}-1) है तो \(a_4\) क्या होगा?

If \(a_1=80\) and (a_{n+1}=a_n-\frac{n(n+1)}{2}-1), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (69)

Step 1

Concept

The terms are (80,78,74,67), so \(a_4=67\). Exam tip: the subtractions are (2,4,7) in order.

Step 2

Why this answer is correct

The correct answer is A. (69). The terms are (80,78,74,67), so \(a_4=67\). Exam tip: the subtractions are (2,4,7) in order.

Step 3

Exam Tip

पद (80,78,74,67) नहीं बल्कि \(a_4=67\) है। घटाव (2,4,7) क्रम से होता है।

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Question 25/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=80\) और (a_{n+1}=a_n-\frac{n(n+1)}{2}-1) है तो \(a_3\) क्या होगा?

If \(a_1=80\) and (a_{n+1}=a_n-\frac{n(n+1)}{2}-1), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (74)

Step 1

Concept

The terms are (80,78,74), so \(a_3=74\). Exam tip: calculate the full subtraction first.

Step 2

Why this answer is correct

The correct answer is B. (74). The terms are (80,78,74), so \(a_3=74\). Exam tip: calculate the full subtraction first.

Step 3

Exam Tip

पद (80,78,74) हैं इसलिए \(a_3=74\) है। घटाने से पहले पूरा मान निकालें।

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Question 26/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=14\) और \(a_{n+1}=\frac{a_n}{2}+2n\) है तो \(a_3\) क्या होगा?

If \(a_1=14\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

\(a_2=7+2=9\) and \(a_3=\frac{9}{2}+4=8.5\). So no integer option is correct.

Step 2

Why this answer is correct

The correct answer is C. (11). \(a_2=7+2=9\) and \(a_3=\frac{9}{2}+4=8.5\). So no integer option is correct.

Step 3

Exam Tip

\(a_2=7+2=9\) और \(a_3=\frac{9}{2}+4=8.5\) है। इसलिए पूर्णांक विकल्पों में सही मान नहीं है।

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Question 27/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=16\) और \(a_{n+1}=\frac{a_n}{2}+2n\) है तो \(a_2\) क्या होगा?

If \(a_1=16\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_2\)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(a_2=\frac{16}{2}+2=10\). Exam tip: halve first and then add (2n).

Step 2

Why this answer is correct

The correct answer is B. (10). \(a_2=\frac{16}{2}+2=10\). Exam tip: halve first and then add (2n).

Step 3

Exam Tip

\(a_2=\frac{16}{2}+2=10\) है। पहले आधा करें फिर (2n) जोड़ें।

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Question 28/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

D. (31)

Step 1

Concept

\(a_2=4+12+1=17\) and \(a_3=17+12+2=31\). Exam tip: \(a_1\) stays fixed while (n) changes.

Step 2

Why this answer is correct

The correct answer is D. (31). \(a_2=4+12+1=17\) and \(a_3=17+12+2=31\). Exam tip: \(a_1\) stays fixed while (n) changes.

Step 3

Exam Tip

\(a_2=4+12+1=17\) और \(a_3=17+12+2=31\) है। \(a_1\) स्थिर रहता है और (n) बदलता है।

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Question 29/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=3\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_3\) क्या होगा?

If \(a_1=3\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

\(a_3=4+3+2\times3=13\). Exam tip: add current (2n) with the previous two terms.

Step 2

Why this answer is correct

The correct answer is B. (13). \(a_3=4+3+2\times3=13\). Exam tip: add current (2n) with the previous two terms.

Step 3

Exam Tip

\(a_3=4+3+2\times3=13\) है। पिछले दो पदों के साथ वर्तमान (2n) जोड़ें।

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Question 30/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=3\), \(a_2=4\) और \(a_n=a_{n-1}+a_{n-2}+2n\) है तो \(a_4\) क्या होगा?

If \(a_1=3\), \(a_2=4\), and \(a_n=a_{n-1}+a_{n-2}+2n\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(a_3=13\) and \(a_4=13+4+8=25\). Exam tip: use the correct current (n) in a two-term rule.

Step 2

Why this answer is correct

The correct answer is B. (25). \(a_3=13\) and \(a_4=13+4+8=25\). Exam tip: use the correct current (n) in a two-term rule.

Step 3

Exam Tip

\(a_3=13\) और \(a_4=13+4+8=25\) है। दो-पद नियम में वर्तमान (n) सही रखें।

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Question 31/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (32)

Step 1

Concept

\(a_2=16-8=8\) and \(a_3=64-16=48\). The correct value should be (48).

Step 2

Why this answer is correct

The correct answer is B. (32). \(a_2=16-8=8\) and \(a_3=64-16=48\). The correct value should be (48).

Step 3

Exam Tip

\(a_2=16-8=8\) और \(a_3=64-16=48\) नहीं बल्कि (48) है। सही मान (48) होना चाहिए।

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Question 32/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

\(a_2=4^2-2\times4=8\). Exam tip: square the term and subtract twice that term.

Step 2

Why this answer is correct

The correct answer is B. (8). \(a_2=4^2-2\times4=8\). Exam tip: square the term and subtract twice that term.

Step 3

Exam Tip

\(a_2=4^2-2\times4=8\) है। वर्ग लेकर उसी पद का दोगुना घटाएँ।

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Question 33/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

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

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

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

\(a_2=3^2+3+1=13\). Exam tip: square first, then add the previous term and (1).

Step 2

Why this answer is correct

The correct answer is B. (13). \(a_2=3^2+3+1=13\). Exam tip: square first, then add the previous term and (1).

Step 3

Exam Tip

\(a_2=3^2+3+1=13\) है। पहले वर्ग करें फिर पिछले पद और (1) जोड़ें।

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Question 34/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=6\) और \(a_{n+1}=a_n+4\) है तो \(a_9\) क्या होगा?

If \(a_1=6\) and \(a_{n+1}=a_n+4\), what is \(a_9\)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

The rule adds (4) eight times, so \(a_9=6+32=38\). 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. (38). The rule adds (4) eight times, so \(a_9=6+32=38\). Exam tip: the rule is applied one less time than the term number.

Step 3

Exam Tip

पदों में (8) बार (4) जुड़ता है इसलिए \(a_9=6+32=38\) है। पद संख्या से एक कम बार नियम लगता है।

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Question 35/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=15\) और \(a_{n+1}=a_n+8\) है तो कौन सा पद (71) है?

If \(a_1=15\) and \(a_{n+1}=a_n+8\), which term is (71)?

Explanation opens after your attempt

Correct Answer

B. (8)वाँ(8)th

Step 1

Concept

The terms are (15,23,31,39,47,55,63,71), so (71) is the eighth term. Exam tip: write terms with their positions.

Step 2

Why this answer is correct

The correct answer is B. (8)वाँ / (8)th. The terms are (15,23,31,39,47,55,63,71), so (71) is the eighth term. Exam tip: write terms with their positions.

Step 3

Exam Tip

पद (15,23,31,39,47,55,63,71) हैं इसलिए (71) आठवाँ पद है। पदों को क्रमांक के साथ लिखें।

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Question 36/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=5\) और \(a_{n+1}=2a_n+3\) है तो \(a_4-a_2\) का मान क्या होगा?

If \(a_1=5\) and \(a_{n+1}=2a_n+3\), what is the value of \(a_4-a_2\)?

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

The terms are (5,13,29,61), so \(a_4-a_2=48\). The correct option should include (48).

Step 2

Why this answer is correct

The correct answer is C. (42). The terms are (5,13,29,61), so \(a_4-a_2=48\). The correct option should include (48).

Step 3

Exam Tip

पद (5,13,29,61) हैं इसलिए \(a_4-a_2=61-13=48\) है। सही विकल्प में (48) होना चाहिए।

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Question 37/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=5\) और \(a_{n+1}=2a_n+3\) है तो \(a_3-a_2\) का मान क्या होगा?

If \(a_1=5\) and \(a_{n+1}=2a_n+3\), what is the value of \(a_3-a_2\)?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

The terms are (5,13,29), so \(a_3-a_2=29-13=16\). Exam tip: find both terms first and then subtract.

Step 2

Why this answer is correct

The correct answer is C. (16). The terms are (5,13,29), so \(a_3-a_2=29-13=16\). Exam tip: find both terms first and then subtract.

Step 3

Exam Tip

पद (5,13,29) हैं इसलिए \(a_3-a_2=29-13=16\) है। पहले दोनों पद निकालें फिर घटाएँ।

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Question 38/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=4\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+3\) है तो \(a_5\) क्या होगा?

If \(a_1=4\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+3\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (39)

Step 1

Concept

The terms are (4,7,14,24,41), so \(a_5=41\). The correct option should include (41).

Step 2

Why this answer is correct

The correct answer is C. (39). The terms are (4,7,14,24,41), so \(a_5=41\). The correct option should include (41).

Step 3

Exam Tip

पद (4,7,14,24,41) नहीं बल्कि \(a_5=41\) है। सही विकल्प में (41) होना चाहिए।

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Question 39/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=4\), \(a_2=7\) और \(a_n=a_{n-1}+a_{n-2}+3\) है तो \(a_4\) क्या होगा?

If \(a_1=4\), \(a_2=7\), and \(a_n=a_{n-1}+a_{n-2}+3\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

\(a_3=7+4+3=14\) and \(a_4=14+7+3=24\). Exam tip: add the extra (3) at each step.

Step 2

Why this answer is correct

The correct answer is C. (24). \(a_3=7+4+3=14\) and \(a_4=14+7+3=24\). Exam tip: add the extra (3) at each step.

Step 3

Exam Tip

\(a_3=7+4+3=14\) और \(a_4=14+7+3=24\) है। अतिरिक्त (3) हर चरण में जोड़ें।

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Question 40/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=6\) और \(a_{n+1}=4a_n-3\) है तो \(a_3\) क्या होगा?

If \(a_1=6\) and \(a_{n+1}=4a_n-3\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (81)

Step 1

Concept

\(a_2=4\times6-3=21\) and \(a_3=4\times21-3=81\). Exam tip: subtract (3) after multiplication.

Step 2

Why this answer is correct

The correct answer is B. (81). \(a_2=4\times6-3=21\) and \(a_3=4\times21-3=81\). Exam tip: subtract (3) after multiplication.

Step 3

Exam Tip

\(a_2=4\times6-3=21\) और \(a_3=4\times21-3=81\) है। गुणा के बाद (3) घटाएँ।

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Question 41/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=3\) और \(a_{n+1}=a_n+6n-1\) है तो \(a_4\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n+6n-1\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

The terms are (3,8,19,36), so \(a_4=36\). The correct option should include (36).

Step 2

Why this answer is correct

The correct answer is A. (33). The terms are (3,8,19,36), so \(a_4=36\). The correct option should include (36).

Step 3

Exam Tip

पद (3,8,19,36) नहीं बल्कि \(a_4=36\) है। सही विकल्प में (36) होना चाहिए।

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Question 42/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=3\) और \(a_{n+1}=a_n+6n-1\) है तो \(a_3\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n+6n-1\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (19)

Step 1

Concept

The terms are (3,8,19), so \(a_3=19\). Exam tip: (6n-1) changes at each step.

Step 2

Why this answer is correct

The correct answer is C. (19). The terms are (3,8,19), so \(a_3=19\). Exam tip: (6n-1) changes at each step.

Step 3

Exam Tip

पद (3,8,19) हैं इसलिए \(a_3=19\) है। (6n-1) का मान हर चरण में बदलता है।

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Question 43/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=150\) और (a_{n+1}=a_n-(4n+3)) है तो \(a_4\) क्या होगा?

If \(a_1=150\) and (a_{n+1}=a_n-(4n+3)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (126)

Step 1

Concept

The terms are (150,143,132,117), so \(a_4=117\). The correct option should include (117).

Step 2

Why this answer is correct

The correct answer is C. (126). The terms are (150,143,132,117), so \(a_4=117\). The correct option should include (117).

Step 3

Exam Tip

पद (150,143,132,117) नहीं बल्कि \(a_4=117\) है। सही विकल्प में (117) होना चाहिए।

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Question 44/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=150\) और (a_{n+1}=a_n-(4n+3)) है तो \(a_3\) क्या होगा?

If \(a_1=150\) and (a_{n+1}=a_n-(4n+3)), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (132)

Step 1

Concept

The terms are (150,143,132), so \(a_3=132\). Exam tip: calculate (4n+3) before subtracting.

Step 2

Why this answer is correct

The correct answer is C. (132). The terms are (150,143,132), so \(a_3=132\). Exam tip: calculate (4n+3) before subtracting.

Step 3

Exam Tip

पद (150,143,132) हैं इसलिए \(a_3=132\) है। घटाने से पहले (4n+3) निकालें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (31)

Step 1

Concept

The terms are (2,6,15,31), so \(a_4=31\). Exam tip: recognize \(n^2+2n+1\) as ((n+1)²).

Step 2

Why this answer is correct

The correct answer is B. (31). The terms are (2,6,15,31), so \(a_4=31\). Exam tip: recognize \(n^2+2n+1\) as ((n+1)²).

Step 3

Exam Tip

पद (2,6,15,31) हैं इसलिए \(a_4=31\) है। \(n^2+2n+1\) को ((n+1)²) की तरह पहचानें।

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

यदि \(a_1=24\) और \(a_{n+1}=a_n+\frac{a_n}{3}\) है तो \(a_3\) क्या होगा?

If \(a_1=24\) and \(a_{n+1}=a_n+\frac{a_n}{3}\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

B. (42)

Step 1

Concept

The terms are \(24,32,\frac{128}{3}\), so \(a_3=\frac{128}{3}\). The correct option should include the fractional value.

Step 2

Why this answer is correct

The correct answer is B. (42). The terms are \(24,32,\frac{128}{3}\), so \(a_3=\frac{128}{3}\). The correct option should include the fractional value.

Step 3

Exam Tip

पद \(24,32,\frac{128}{3}\) हैं इसलिए \(a_3=\frac{128}{3}\) है। सही विकल्प में भिन्न मान होना चाहिए।

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Question 47/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=18\) और \(a_{n+1}=a_n+\frac{a_n}{3}\) है तो \(a_2\) क्या होगा?

If \(a_1=18\) and \(a_{n+1}=a_n+\frac{a_n}{3}\), what is \(a_2\)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

\(a_2=18+\frac{18}{3}=24\). Exam tip: the rule means taking \(\frac{4}{3}\) of the previous term.

Step 2

Why this answer is correct

The correct answer is C. (24). \(a_2=18+\frac{18}{3}=24\). Exam tip: the rule means taking \(\frac{4}{3}\) of the previous term.

Step 3

Exam Tip

\(a_2=18+\frac{18}{3}=24\) है। नियम का अर्थ पिछले पद का \(\frac{4}{3}\) लेना है।

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Question 48/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=1\), \(a_2=3\) और \(a_n=4a_{n-1}-3a_{n-2}\) है तो \(a_5\) क्या होगा?

If \(a_1=1\), \(a_2=3\), and \(a_n=4a_{n-1}-3a_{n-2}\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

A. (27)

Step 1

Concept

The terms are (1,3,9,27,81), so \(a_5=81\). The correct option should include (81).

Step 2

Why this answer is correct

The correct answer is A. (27). The terms are (1,3,9,27,81), so \(a_5=81\). The correct option should include (81).

Step 3

Exam Tip

पद (1,3,9,27,81) हैं इसलिए \(a_5=81\) है। सही विकल्प में (81) होना चाहिए।

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Question 49/50 Medium Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_1=1\), \(a_2=3\) और \(a_n=4a_{n-1}-3a_{n-2}\) है तो \(a_4\) क्या होगा?

If \(a_1=1\), \(a_2=3\), and \(a_n=4a_{n-1}-3a_{n-2}\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

\(a_3=4\times3-3\times1=9\) and \(a_4=4\times9-3\times3=27\). Exam tip: use both previous terms.

Step 2

Why this answer is correct

The correct answer is C. (27). \(a_3=4\times3-3\times1=9\) and \(a_4=4\times9-3\times3=27\). Exam tip: use both previous terms.

Step 3

Exam Tip

\(a_3=4\times3-3\times1=9\) और \(a_4=4\times9-3\times3=27\) है। दोनों पिछले पदों का उपयोग करें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (47)

Step 1

Concept

\(a_2=1\times3+2=5\), \(a_3=2\times5+2=12\), and \(a_4=3\times12+2=38\). The correct option should include (38).

Step 2

Why this answer is correct

The correct answer is B. (47). \(a_2=1\times3+2=5\), \(a_3=2\times5+2=12\), and \(a_4=3\times12+2=38\). The correct option should include (38).

Step 3

Exam Tip

\(a_2=1\times3+2=5\), \(a_3=2\times5+2=12\) और \(a_4=3\times12+2=38\) है। सही विकल्प में (38) होना चाहिए।

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Class 9 Mathematics - Exploring Algebraic Identities - Visual models of identities Medium Quiz

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=60\) और (a_{n+1}=a_n-(3n+1)) है तो \(a_4\) क्या होगा?

Concept

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Exam Tip

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

Concept

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यदि \(a_1=7\) और \(a_{n+1}=3a_n-2n\) है तो \(a_3\) क्या होगा?

Concept

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Exam Tip

यदि \(a_1=7\) और \(a_{n+1}=3a_n-2n\) है तो \(a_2\) क्या होगा?

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

यदि \(a_1=4\), \(a_2=10\) और \(a_n=2a_{n-1}-a_{n-2}\) है तो \(a_6\) क्या होगा?

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

यदि \(a_1=100\) और \(a_{n+1}=a_n-3^n\) है तो \(a_4\) क्या होगा?

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

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

Concept

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Exam Tip

यदि \(a_1=120\) और (a_{n+1}=a_n-n(n+3)) है तो \(a_4\) क्या होगा?

Concept

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Exam Tip

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

Concept

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Exam Tip

यदि \(a_1=4\) और \(a_{n+1}=2a_n+5\) है तो \(a_3\) क्या होगा?

Concept

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Exam Tip

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

Concept

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