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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

Question 1/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

C. (126)

Step 1

Concept

The terms are (4,13,41,126), so \(a_4=126\). Exam tip: find \(3a_n\) first and then add (n).

Step 2

Why this answer is correct

The correct answer is C. (126). The terms are (4,13,41,126), so \(a_4=126\). Exam tip: find \(3a_n\) first and then add (n).

Step 3

Exam Tip

पद (4,13,41,126) हैं इसलिए \(a_4=126\) है। हर चरण में पहले \(3a_n\) निकालें फिर (n) जोड़ें।

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Question 2/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

किसी अनुक्रम में \(a_1=3\) और \(a_n=2a_{n-1}+1\) है। \(a_4\) का मान क्या होगा?

In a sequence, \(a_1=3\) and \(a_n=2a_{n-1}+1\). What will be the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. इकतीस(31)

Step 1

Concept

First \(a_2=7\), then \(a_3=15\), and finally \(a_4=31\). In exams, apply the recursive rule step by step.

Step 2

Why this answer is correct

The correct answer is C. इकतीस / (31). First \(a_2=7\), then \(a_3=15\), and finally \(a_4=31\). In exams, apply the recursive rule step by step.

Step 3

Exam Tip

पहले \(a_2=7\), फिर \(a_3=15\) और अंत में \(a_4=31\) मिलता है। परीक्षा में पुनरावर्ती नियम को क्रम से लागू करें।

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Question 3/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=150\) और (a_{n+1}=a_n-\(n^2+2n\)) है तो \(a_5\) क्या होगा?

If \(a_1=150\) and (a_{n+1}=a_n-\(n^2+2n\)), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (100)

Step 1

Concept

The subtracted values are (3,8,15,24), so \(a_5=100\). Exam tip: write all changing subtractions separately first.

Step 2

Why this answer is correct

The correct answer is B. (100). The subtracted values are (3,8,15,24), so \(a_5=100\). Exam tip: write all changing subtractions separately first.

Step 3

Exam Tip

घटने वाले मान (3,8,15,24) हैं इसलिए \(a_5=100\) है। पहले सभी बदलते घटावों को अलग लिखें।

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Question 4/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

किसी अनुक्रम में \(t_1=2\), \(t_2=5\) और \(t_n=t_{n-1}+2t_{n-2}\) है। \(t_5\) का मान क्या होगा?

In a sequence, \(t_1=2\), \(t_2=5\), and \(t_n=t_{n-1}+2t_{n-2}\). What will be the value of \(t_5\)?

Explanation opens after your attempt

Correct Answer

D. सैंतीस(37)

Step 1

Concept

We get \(t_3=9\), \(t_4=19\), and \(t_5=37\). In exams, use the previous two terms carefully.

Step 2

Why this answer is correct

The correct answer is D. सैंतीस / (37). We get \(t_3=9\), \(t_4=19\), and \(t_5=37\). In exams, use the previous two terms carefully.

Step 3

Exam Tip

\(t_3=9\), \(t_4=19\) और \(t_5=37\) मिलता है। परीक्षा में पिछले दो पदों का सही उपयोग करें।

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Question 5/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+3a_{n-2}\) है तो \(a_5\) क्या होगा?

If \(a_1=2\), \(a_2=5\), and \(a_n=2a_{n-1}+3a_{n-2}\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (142)

Step 1

Concept

The terms are (2,5,16,47,142), so \(a_5=142\). Exam tip: apply the correct coefficient to each previous term.

Step 2

Why this answer is correct

The correct answer is B. (142). The terms are (2,5,16,47,142), so \(a_5=142\). Exam tip: apply the correct coefficient to each previous term.

Step 3

Exam Tip

पद (2,5,16,47,142) हैं इसलिए \(a_5=142\) है। दोनों पिछले पदों पर सही गुणांक लगाएँ।

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Question 6/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

\(a_3=11\) and \(a_4=34\). Exam tip: do not forget to add the current (n) in a two-term rule.

Step 2

Why this answer is correct

The correct answer is B. (34). \(a_3=11\) and \(a_4=34\). Exam tip: do not forget to add the current (n) in a two-term rule.

Step 3

Exam Tip

\(a_3=11\) और \(a_4=34\) है। दो-पद नियम में वर्तमान (n) भी जोड़ना न भूलें।

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Question 7/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

C. (110)

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 8/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

The added values are (3,8,17,32), so \(a_5=66\). Exam tip: calculate the power and square separately.

Step 2

Why this answer is correct

The correct answer is C. (66). The added values are (3,8,17,32), so \(a_5=66\). Exam tip: calculate the power and square separately.

Step 3

Exam Tip

जुड़ने वाले मान (3,8,17,32) हैं इसलिए \(a_5=66\) है। घात और वर्ग अलग-अलग निकालें।

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

यदि \(a_1=200\) और (a_{n+1}=a_n-\(3^n+n\)) है तो \(a_4\) क्या होगा?

If \(a_1=200\) and (a_{n+1}=a_n-\(3^n+n\)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (155)

Step 1

Concept

The subtracted values are (4,11,30), so \(a_4=155\). Exam tip: first calculate the full value of \(3^n+n\).

Step 2

Why this answer is correct

The correct answer is A. (155). The subtracted values are (4,11,30), so \(a_4=155\). Exam tip: first calculate the full value of \(3^n+n\).

Step 3

Exam Tip

घटने वाले मान (4,11,30) हैं इसलिए \(a_4=155\) है। \(3^n+n\) को पहले पूरा निकालें।

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Question 10/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

A. (48)

Step 1

Concept

The added values are (2,4,9,28), so \(a_5=48\). Exam tip: add both the factorial and (n).

Step 2

Why this answer is correct

The correct answer is A. (48). The added values are (2,4,9,28), so \(a_5=48\). Exam tip: add both the factorial and (n).

Step 3

Exam Tip

जुड़ने वाले मान (2,4,9,28) हैं इसलिए \(a_5=48\) है। फैक्टोरियल और (n) दोनों जोड़ें।

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Question 11/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=90\) और (a_{n+1}=a_n-(n!+2n)) है तो \(a_5\) क्या होगा?

If \(a_1=90\) and (a_{n+1}=a_n-(n!+2n)), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (37)

Step 1

Concept

The subtracted values are (3,6,12,32), so \(a_5=37\). Exam tip: write each subtraction in order.

Step 2

Why this answer is correct

The correct answer is C. (37). The subtracted values are (3,6,12,32), so \(a_5=37\). Exam tip: write each subtraction in order.

Step 3

Exam Tip

घटने वाले मान (3,6,12,32) हैं इसलिए \(a_5=37\) है। हर घटाव को क्रम से लिखें।

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Question 12/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (37)

Step 1

Concept

\(a_2=10\) and \(a_3=37\). Exam tip: multiply first and then subtract (n+1).

Step 2

Why this answer is correct

The correct answer is B. (37). \(a_2=10\) and \(a_3=37\). Exam tip: multiply first and then subtract (n+1).

Step 3

Exam Tip

\(a_2=10\) और \(a_3=37\) है। गुणा के बाद (n+1) घटाएँ।

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Question 13/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

C. (47)

Step 1

Concept

\(a_3=19\) and \(a_4=47\). Exam tip: also add \(n^2\) in the two-term rule.

Step 2

Why this answer is correct

The correct answer is C. (47). \(a_3=19\) and \(a_4=47\). Exam tip: also add \(n^2\) in the two-term rule.

Step 3

Exam Tip

\(a_3=19\) और \(a_4=47\) है। दो-पद नियम में \(n^2\) भी जोड़ें।

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Question 14/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=5\), \(a_2=11\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_5\) क्या होगा?

If \(a_1=5\), \(a_2=11\), and \(a_n=3a_{n-1}-2a_{n-2}\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (95)

Step 1

Concept

The terms are (5,11,23,47,95), so \(a_5=95\). Exam tip: keep the order of multiplication and subtraction correct.

Step 2

Why this answer is correct

The correct answer is C. (95). The terms are (5,11,23,47,95), so \(a_5=95\). Exam tip: keep the order of multiplication and subtraction correct.

Step 3

Exam Tip

पद (5,11,23,47,95) हैं इसलिए \(a_5=95\) है। गुणा और घटाव का क्रम सही रखें।

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Question 15/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

The added values are (5,12,23), so \(a_4=48\). Exam tip: calculate both the product and the power.

Step 2

Why this answer is correct

The correct answer is C. (48). The added values are (5,12,23), so \(a_4=48\). Exam tip: calculate both the product and the power.

Step 3

Exam Tip

जुड़ने वाले मान (5,12,23) हैं इसलिए \(a_4=48\) है। गुणनफल और घात दोनों निकालें।

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Question 16/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=180\) और (a_{n+1}=a_n-(n(n+2)+2^n)) है तो \(a_4\) क्या होगा?

If \(a_1=180\) and (a_{n+1}=a_n-(n(n+2)+2^n)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (140)

Step 1

Concept

The subtracted values are (5,12,23), so \(a_4=140\). Exam tip: calculate the full value before subtracting.

Step 2

Why this answer is correct

The correct answer is C. (140). The subtracted values are (5,12,23), so \(a_4=140\). Exam tip: calculate the full value before subtracting.

Step 3

Exam Tip

घटने वाले मान (5,12,23) हैं इसलिए \(a_4=140\) है। घटाने से पहले पूरा मान निकालें।

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Question 17/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=9\) और \(a_{n+1}=2a_n+3n-2\) है तो \(a_3\) क्या होगा?

If \(a_1=9\) and \(a_{n+1}=2a_n+3n-2\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

The terms are (9,19,42), so \(a_3=42\). Exam tip: double the previous term first and then add (3n-2).

Step 2

Why this answer is correct

The correct answer is C. (42). The terms are (9,19,42), so \(a_3=42\). Exam tip: double the previous term first and then add (3n-2).

Step 3

Exam Tip

पद (9,19,42) हैं इसलिए \(a_3=42\) है। पहले पिछले पद को दोगुना करें फिर (3n-2) जोड़ें।

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Question 18/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=30\) और \(a_{n+1}=\frac{a_n}{3}+2n^2\) है तो \(a_3\) क्या होगा?

If \(a_1=30\) and \(a_{n+1}=\frac{a_n}{3}+2n^2\), what is \(a_3\)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(a_2=12\) and \(a_3=12\). Exam tip: divide first and then add \(2n^2\).

Step 2

Why this answer is correct

The correct answer is A. (12). \(a_2=12\) and \(a_3=12\). Exam tip: divide first and then add \(2n^2\).

Step 3

Exam Tip

\(a_2=12\) और \(a_3=12\) है। भाग के बाद \(2n^2\) जोड़ें।

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Question 19/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (40)

Step 1

Concept

\(a_2=21\) and \(a_3=40\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 2

Why this answer is correct

The correct answer is B. (40). \(a_2=21\) and \(a_3=40\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 3

Exam Tip

\(a_2=21\) और \(a_3=40\) है। \(a_1\) स्थिर रहता है जबकि \(n^2\) बदलता है।

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Question 20/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

D. (61)

Step 1

Concept

The terms are (2,4,15,31,61), so \(a_5=61\). Exam tip: add current (3n) with the previous two terms.

Step 2

Why this answer is correct

The correct answer is D. (61). The terms are (2,4,15,31,61), so \(a_5=61\). Exam tip: add current (3n) with the previous two terms.

Step 3

Exam Tip

पद (2,4,15,31,61) हैं इसलिए \(a_5=61\) है। पिछले दो पदों के साथ वर्तमान (3n) जोड़ें।

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Question 21/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

\(a_3=21\) and \(a_4=63\). Exam tip: after applying coefficients, also add \(n^2\).

Step 2

Why this answer is correct

The correct answer is A. (63). \(a_3=21\) and \(a_4=63\). Exam tip: after applying coefficients, also add \(n^2\).

Step 3

Exam Tip

\(a_3=21\) और \(a_4=63\) है। गुणांक लगाने के बाद \(n^2\) भी जोड़ें।

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Question 22/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (39)

Step 1

Concept

\(a_2=7\) and \(a_3=39\). Exam tip: square, subtract \(2a_n\), and add (4).

Step 2

Why this answer is correct

The correct answer is B. (39). \(a_2=7\) and \(a_3=39\). Exam tip: square, subtract \(2a_n\), and add (4).

Step 3

Exam Tip

\(a_2=7\) और \(a_3=39\) है। वर्ग निकालकर \(2a_n\) घटाएँ और (4) जोड़ें।

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Question 23/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

D. (14)

Step 1

Concept

\(a_2=4^2-4+2=14\). Exam tip: square the term, subtract it, and add (2).

Step 2

Why this answer is correct

The correct answer is D. (14). \(a_2=4^2-4+2=14\). Exam tip: square the term, subtract it, and add (2).

Step 3

Exam Tip

\(a_2=4^2-4+2=14\) है। वर्ग लेकर वही पद घटाएँ और (2) जोड़ें।

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Question 24/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=13\) और \(a_{n+1}=a_n+6\) है तो कौन सा पद (79) है?

If \(a_1=13\) and \(a_{n+1}=a_n+6\), which term is (79)?

Explanation opens after your attempt

Correct Answer

A. (12)वाँ(12)th

Step 1

Concept

(79-13=66), and \(66\div6=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.

Step 2

Why this answer is correct

The correct answer is A. (12)वाँ / (12)th. (79-13=66), and \(66\div6=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.

Step 3

Exam Tip

(79-13=66) और \(66\div6=11\) चरण हैं इसलिए पद संख्या (12) है। चरणों में (1) जोड़कर पद संख्या मिलती है।

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Question 25/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=8\) और \(a_{n+1}=a_n+9\) है तो \(a_{12}\) क्या होगा?

If \(a_1=8\) and \(a_{n+1}=a_n+9\), what is \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

B. (107)

Step 1

Concept

For \(a_{12}\), (9) is added (11) times, so \(a_{12}=107\). Exam tip: the rule is applied one less time than the term number.

Step 2

Why this answer is correct

The correct answer is B. (107). For \(a_{12}\), (9) is added (11) times, so \(a_{12}=107\). Exam tip: the rule is applied one less time than the term number.

Step 3

Exam Tip

\(a_{12}\) के लिए (9) को (11) बार जोड़ा जाता है इसलिए \(a_{12}=107\) है। पद संख्या से एक कम बार नियम लगता है।

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Question 26/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

D. (78)

Step 1

Concept

The terms are (4,17,43,95), so \(a_4-a_2=78\). Exam tip: find both terms first and then subtract.

Step 2

Why this answer is correct

The correct answer is D. (78). The terms are (4,17,43,95), so \(a_4-a_2=78\). Exam tip: find both terms first and then subtract.

Step 3

Exam Tip

पद (4,17,43,95) हैं इसलिए \(a_4-a_2=78\) है। पहले दोनों पद निकालें फिर घटाएँ।

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Question 27/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=3\), \(a_2=9\) और \(a_n=a_{n-1}+a_{n-2}+7\) है तो \(a_5\) क्या होगा?

If \(a_1=3\), \(a_2=9\), and \(a_n=a_{n-1}+a_{n-2}+7\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

A. (61)

Step 1

Concept

The terms are (3,9,19,35,61), so \(a_5=61\). Exam tip: also add (7) with the previous two terms.

Step 2

Why this answer is correct

The correct answer is A. (61). The terms are (3,9,19,35,61), so \(a_5=61\). Exam tip: also add (7) with the previous two terms.

Step 3

Exam Tip

पद (3,9,19,35,61) हैं इसलिए \(a_5=61\) है। पिछले दो पदों के साथ (7) भी जोड़ें।

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Question 28/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

\(a_2=10\) and \(a_3=66\). Exam tip: multiply by (7) first and then subtract (4).

Step 2

Why this answer is correct

The correct answer is B. (66). \(a_2=10\) and \(a_3=66\). Exam tip: multiply by (7) first and then subtract (4).

Step 3

Exam Tip

\(a_2=10\) और \(a_3=66\) है। पहले (7) से गुणा करें फिर (4) घटाएँ।

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Question 29/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=6\) और \(a_{n+1}=a_n+9n-4\) है तो \(a_4\) क्या होगा?

If \(a_1=6\) and \(a_{n+1}=a_n+9n-4\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

D. (48)

Step 1

Concept

The added values are (5,14,23), so \(a_4=48\). Exam tip: (9n-4) changes at each step.

Step 2

Why this answer is correct

The correct answer is D. (48). The added values are (5,14,23), so \(a_4=48\). Exam tip: (9n-4) changes at each step.

Step 3

Exam Tip

जुड़ने वाले मान (5,14,23) हैं इसलिए \(a_4=48\) है। (9n-4) का मान हर चरण में बदलता है।

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Question 30/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=210\) और (a_{n+1}=a_n-(7n+6)) है तो \(a_4\) क्या होगा?

If \(a_1=210\) and (a_{n+1}=a_n-(7n+6)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (150)

Step 1

Concept

The subtracted values are (13,20,27), so \(a_4=150\). Exam tip: calculate (7n+6) before subtracting.

Step 2

Why this answer is correct

The correct answer is A. (150). The subtracted values are (13,20,27), so \(a_4=150\). Exam tip: calculate (7n+6) before subtracting.

Step 3

Exam Tip

घटने वाले मान (13,20,27) हैं इसलिए \(a_4=150\) है। घटाने से पहले (7n+6) निकालें।

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Question 31/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=2\), \(a_2=3\) और \(a_n=5a_{n-1}-4a_{n-2}+3\) है तो \(a_4\) क्या होगा?

If \(a_1=2\), \(a_2=3\), and \(a_n=5a_{n-1}-4a_{n-2}+3\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (41)

Step 1

Concept

\(a_3=10\) and \(a_4=41\). Exam tip: apply the coefficients of both previous terms carefully.

Step 2

Why this answer is correct

The correct answer is C. (41). \(a_3=10\) and \(a_4=41\). Exam tip: apply the coefficients of both previous terms carefully.

Step 3

Exam Tip

\(a_3=10\) और \(a_4=41\) है। दोनों पिछले पदों के गुणांक सावधानी से लगाएँ।

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Question 32/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (42)

Step 1

Concept

The total addition is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=42\). Exam tip: find total fractional addition first.

Step 2

Why this answer is correct

The correct answer is B. (42). The total addition is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=42\). Exam tip: find total fractional addition first.

Step 3

Exam Tip

कुल जोड़ (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=42\) है। भिन्न जोड़ में कुल जोड़ पहले निकालें।

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Question 33/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=80\) और \(a_{n+1}=a_n-\frac{7n}{2}\) है तो \(a_5\) क्या होगा?

If \(a_1=80\) and \(a_{n+1}=a_n-\frac{7n}{2}\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

A. (45)

Step 1

Concept

The total subtraction is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=45\). Exam tip: add fractional subtractions first.

Step 2

Why this answer is correct

The correct answer is A. (45). The total subtraction is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=45\). Exam tip: add fractional subtractions first.

Step 3

Exam Tip

कुल घटाव (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=45\) है। भिन्न घटावों को पहले जोड़ें।

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Question 34/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

D. (74)

Step 1

Concept

\(a_2=9\), \(a_3=23\), and \(a_4=74\). Exam tip: the multiplier (n) changes at each step.

Step 2

Why this answer is correct

The correct answer is D. (74). \(a_2=9\), \(a_3=23\), and \(a_4=74\). Exam tip: the multiplier (n) changes at each step.

Step 3

Exam Tip

\(a_2=9\), \(a_3=23\) और \(a_4=74\) है। गुणक (n) हर चरण में बदलता है।

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Question 35/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (274)

Step 1

Concept

\(a_2=14\), \(a_3=55\), and \(a_4=274\). Exam tip: the multiplier (n+2) changes.

Step 2

Why this answer is correct

The correct answer is B. (274). \(a_2=14\), \(a_3=55\), and \(a_4=274\). Exam tip: the multiplier (n+2) changes.

Step 3

Exam Tip

\(a_2=14\), \(a_3=55\) और \(a_4=274\) है। गुणक (n+2) बदलता है।

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Question 36/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

अनुक्रम \(4,14,44,134,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence \(4,14,44,134,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(a_1=4, a_{n+1}=3a_n+2\)

Step 1

Concept

\(3\times4+2=14\) and \(3\times14+2=44\). Exam tip: check the first term too when selecting a rule.

Step 2

Why this answer is correct

The correct answer is C. \(a_1=4, a_{n+1}=3a_n+2\). \(3\times4+2=14\) and \(3\times14+2=44\). Exam tip: check the first term too when selecting a rule.

Step 3

Exam Tip

\(3\times4+2=14\) और \(3\times14+2=44\) है। नियम चुनते समय पहला पद भी जाँचें।

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Question 37/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

अनुक्रम \(6,11,19,30,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence \(6,11,19,30,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_1=6, a_{n+1}=a_n+3n+2\)

Step 1

Concept

The additions are (5,8,11), so (3n+2) is added. Exam tip: match both the first term and changing additions.

Step 2

Why this answer is correct

The correct answer is D. \(a_1=6, a_{n+1}=a_n+3n+2\). The additions are (5,8,11), so (3n+2) is added. Exam tip: match both the first term and changing additions.

Step 3

Exam Tip

जोड़ (5,8,11) हैं इसलिए (3n+2) जुड़ता है। पहला पद और बदलते जोड़ दोनों मिलाएँ।

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Question 38/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=5\) और \(a_{n+1}=a_n+n^2\) है तो कौन सा पद (60) है?

If \(a_1=5\) and \(a_{n+1}=a_n+n^2\), which term is (60)?

Explanation opens after your attempt

Correct Answer

A. (6)वाँ(6)th

Step 1

Concept

The terms are (5,6,10,19,35,60), so (60) is the sixth term. Exam tip: write positions while adding squares.

Step 2

Why this answer is correct

The correct answer is A. (6)वाँ / (6)th. The terms are (5,6,10,19,35,60), so (60) is the sixth term. Exam tip: write positions while adding squares.

Step 3

Exam Tip

पद (5,6,10,19,35,60) हैं इसलिए (60) छठा पद है। वर्ग जोड़ते समय क्रमांक साथ लिखें।

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Question 39/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

B. (68)

Step 1

Concept

The added values are (3,6,14,40), so \(a_5=68\). Exam tip: calculate both the factorial and the power.

Step 2

Why this answer is correct

The correct answer is B. (68). The added values are (3,6,14,40), so \(a_5=68\). Exam tip: calculate both the factorial and the power.

Step 3

Exam Tip

जुड़ने वाले मान (3,6,14,40) हैं इसलिए \(a_5=68\) है। फैक्टोरियल और घात दोनों निकालें।

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Question 40/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

D. (57)

Step 1

Concept

The subtracted values are (3,6,14,40), so \(a_5=57\). Exam tip: find the sum of all subtractions first.

Step 2

Why this answer is correct

The correct answer is D. (57). The subtracted values are (3,6,14,40), so \(a_5=57\). Exam tip: find the sum of all subtractions first.

Step 3

Exam Tip

घटने वाले मान (3,6,14,40) हैं इसलिए \(a_5=57\) है। पूरे घटावों का योग पहले निकालें।

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Question 41/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

A. (23)

Step 1

Concept

The terms are (4,5,15,23), so \(a_4=23\). Exam tip: double first and then add the signed part.

Step 2

Why this answer is correct

The correct answer is A. (23). The terms are (4,5,15,23), so \(a_4=23\). Exam tip: double first and then add the signed part.

Step 3

Exam Tip

पद (4,5,15,23) हैं इसलिए \(a_4=23\) है। दोगुना करने के बाद चिह्न वाला भाग जोड़ें।

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Question 42/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=50\) और (a_{n+1}=a_n-(-1)^n\(n^2+1\)) है तो \(a_4\) क्या होगा?

If \(a_1=50\) and (a_{n+1}=a_n-(-1)^n\(n^2+1\)), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (57)

Step 1

Concept

The terms are (50,52,47,57), so \(a_4=57\). Exam tip: track the outside minus sign with ((-1)^n).

Step 2

Why this answer is correct

The correct answer is B. (57). The terms are (50,52,47,57), so \(a_4=57\). Exam tip: track the outside minus sign with ((-1)^n).

Step 3

Exam Tip

पद (50,52,47,57) हैं इसलिए \(a_4=57\) है। बाहरी ऋण और ((-1)^n) को साथ में देखें।

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Question 43/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

D. (126)

Step 1

Concept

The terms are (2,5,18,49,126), so \(a_5=126\). Exam tip: add the current (2n) at each step.

Step 2

Why this answer is correct

The correct answer is D. (126). The terms are (2,5,18,49,126), so \(a_5=126\). Exam tip: add the current (2n) at each step.

Step 3

Exam Tip

पद (2,5,18,49,126) हैं इसलिए \(a_5=126\) है। वर्तमान (2n) को हर चरण में जोड़ें।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (44)

Step 1

Concept

The terms are (6,14,26,44), so \(a_4=44\). Exam tip: \(a_1\) is fixed while (n(n+1)) changes.

Step 2

Why this answer is correct

The correct answer is A. (44). The terms are (6,14,26,44), so \(a_4=44\). Exam tip: \(a_1\) is fixed while (n(n+1)) changes.

Step 3

Exam Tip

पद (6,14,26,44) हैं इसलिए \(a_4=44\) है। \(a_1\) स्थिर है और (n(n+1)) बदलता है।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (86)

Step 1

Concept

The added values are (9,25,49), so \(a_4=86\). Exam tip: add the odd squares in order.

Step 2

Why this answer is correct

The correct answer is B. (86). The added values are (9,25,49), so \(a_4=86\). Exam tip: add the odd squares in order.

Step 3

Exam Tip

जुड़ने वाले मान (9,25,49) हैं इसलिए \(a_4=86\) है। विषम वर्गों को क्रम से जोड़ें।

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

यदि \(a_1=180\) और (a_{n+1}=a_n-(2n+1)²) है तो \(a_4\) क्या होगा?

If \(a_1=180\) and (a_{n+1}=a_n-(2n+1)²), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

D. (97)

Step 1

Concept

The subtracted squares are (9,25,49), so \(a_4=97\). Exam tip: finding the sum of squares first is easier.

Step 2

Why this answer is correct

The correct answer is D. (97). The subtracted squares are (9,25,49), so \(a_4=97\). Exam tip: finding the sum of squares first is easier.

Step 3

Exam Tip

घटने वाले वर्ग (9,25,49) हैं इसलिए \(a_4=97\) है। पहले वर्गों का योग निकालना आसान है।

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Question 47/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

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

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

Explanation opens after your attempt

Correct Answer

A. (103)

Step 1

Concept

The cube additions are (1,8,27,64), so \(a_5=103\). Exam tip: add the new value of \(n^3\) at each step.

Step 2

Why this answer is correct

The correct answer is A. (103). The cube additions are (1,8,27,64), so \(a_5=103\). Exam tip: add the new value of \(n^3\) at each step.

Step 3

Exam Tip

घन जोड़ (1,8,27,64) हैं इसलिए \(a_5=103\) है। हर चरण में \(n^3\) का नया मान जोड़ें।

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Question 48/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

यदि \(a_1=150\) और \(a_{n+1}=a_n-n^3\) है तो \(a_5\) क्या होगा?

If \(a_1=150\) and \(a_{n+1}=a_n-n^3\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (50)

Step 1

Concept

The subtracted cubes are (1,8,27,64), so \(a_5=50\). Exam tip: find the sum of cubes first.

Step 2

Why this answer is correct

The correct answer is B. (50). The subtracted cubes are (1,8,27,64), so \(a_5=50\). Exam tip: find the sum of cubes first.

Step 3

Exam Tip

घटने वाले घन (1,8,27,64) हैं इसलिए \(a_5=50\) है। घनों का योग पहले निकालें।

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Question 49/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 44

अनुक्रम \(3,8,19,46,\ldots\) के लिए कौन सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence \(3,8,19,46,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_1=3, a_2=8, a_n=2a_{n-1}+a_{n-2}\)

Step 1

Concept

\(2\times8+3=19\) and \(2\times19+8=46\). Exam tip: both starting terms must be correct in a two-term rule.

Step 2

Why this answer is correct

The correct answer is D. \(a_1=3, a_2=8, a_n=2a_{n-1}+a_{n-2}\). \(2\times8+3=19\) and \(2\times19+8=46\). Exam tip: both starting terms must be correct in a two-term rule.

Step 3

Exam Tip

\(2\times8+3=19\) और \(2\times19+8=46\) है। दो-पद नियम में दोनों शुरुआती पद सही होने चाहिए।

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

यदि \(a_1=4\), \(a_2=6\) और \(a_n=a_{n-1}+3a_{n-2}+n\) है तो \(a_4\) क्या होगा?

If \(a_1=4\), \(a_2=6\), and \(a_n=a_{n-1}+3a_{n-2}+n\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

A. (43)

Step 1

Concept

\(a_3=21\) and \(a_4=43\). Exam tip: multiply \(a_{n-2}\) by (3) and add current (n).

Step 2

Why this answer is correct

The correct answer is A. (43). \(a_3=21\) and \(a_4=43\). Exam tip: multiply \(a_{n-2}\) by (3) and add current (n).

Step 3

Exam Tip

\(a_3=21\) और \(a_4=43\) है। \(a_{n-2}\) को (3) से गुणा करके वर्तमान (n) जोड़ें।

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Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Expert Quiz

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

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(a_1=3\) और \(a_n=2a_{n-1}+1\) है। \(a_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=150\) और (a_{n+1}=a_n-\(n^2+2n\)) है तो \(a_5\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(t_1=2\), \(t_2=5\) और \(t_n=t_{n-1}+2t_{n-2}\) है। \(t_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=2\), \(a_2=5\) और \(a_n=2a_{n-1}+3a_{n-2}\) है तो \(a_5\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=200\) और (a_{n+1}=a_n-\(3^n+n\)) है तो \(a_4\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=90\) और (a_{n+1}=a_n-(n!+2n)) है तो \(a_5\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=5\), \(a_2=11\) और \(a_n=3a_{n-1}-2a_{n-2}\) है तो \(a_5\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=180\) और (a_{n+1}=a_n-(n(n+2)+2^n)) है तो \(a_4\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=9\) और \(a_{n+1}=2a_n+3n-2\) है तो \(a_3\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_1=30\) और \(a_{n+1}=\frac{a_n}{3}+2n^2\) है तो \(a_3\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct