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

Mathematics Sequences and Progressions Recursive rule Expert Class 9 Topic Quiz

Topic Quiz • 151 questions • 25 seconds per question.

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Question 1/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 41

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

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

Explanation opens after your attempt
Correct Answer

C. (71)

Explanation

Simple Explanation

\(a_2=5\), \(a_3=17\) और \(a_4=71\) है। गुणक (n+1) हर चरण में बदलता है। / \(a_2=5\), \(a_3=17\), and \(a_4=71\). Exam tip: the multiplier (n+1) changes at every step.

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Question 2/151 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)

Explanation

Simple Explanation

पद (4,13,41,126) हैं इसलिए \(a_4=126\) है। हर चरण में पहले \(3a_n\) निकालें फिर (n) जोड़ें। / The terms are (4,13,41,126), so \(a_4=126\). Exam tip: find \(3a_n\) first and then add (n).

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Question 3/151 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)

Explanation

Simple Explanation

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

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Question 4/151 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)

Explanation

Simple Explanation

घटने वाले मान (3,8,15,24) हैं इसलिए \(a_5=100\) है। पहले सभी बदलते घटावों को अलग लिखें। / The subtracted values are (3,8,15,24), so \(a_5=100\). Exam tip: write all changing subtractions separately first.

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Question 5/151 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)

Explanation

Simple Explanation

\(t_3=9\), \(t_4=19\) और \(t_5=37\) मिलता है। परीक्षा में पिछले दो पदों का सही उपयोग करें। / We get \(t_3=9\), \(t_4=19\), and \(t_5=37\). In exams, use the previous two terms carefully.

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Question 6/151 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)

Explanation

Simple Explanation

पद (2,5,16,47,142) हैं इसलिए \(a_5=142\) है। दोनों पिछले पदों पर सही गुणांक लगाएँ। / The terms are (2,5,16,47,142), so \(a_5=142\). Exam tip: apply the correct coefficient to each previous term.

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Question 7/151 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)

Explanation

Simple Explanation

\(a_3=11\) और \(a_4=34\) है। दो-पद नियम में वर्तमान (n) भी जोड़ना न भूलें। / \(a_3=11\) and \(a_4=34\). Exam tip: do not forget to add the current (n) in a two-term rule.

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Question 8/151 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)

Explanation

Simple Explanation

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

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Question 9/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (3,8,17,32) हैं इसलिए \(a_5=66\) है। घात और वर्ग अलग-अलग निकालें। / The added values are (3,8,17,32), so \(a_5=66\). Exam tip: calculate the power and square separately.

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Question 10/151 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)

Explanation

Simple Explanation

घटने वाले मान (4,11,30) हैं इसलिए \(a_4=155\) है। \(3^n+n\) को पहले पूरा निकालें। / The subtracted values are (4,11,30), so \(a_4=155\). Exam tip: first calculate the full value of \(3^n+n\).

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Question 11/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (2,4,9,28) हैं इसलिए \(a_5=48\) है। फैक्टोरियल और (n) दोनों जोड़ें। / The added values are (2,4,9,28), so \(a_5=48\). Exam tip: add both the factorial and (n).

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Question 12/151 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)

Explanation

Simple Explanation

घटने वाले मान (3,6,12,32) हैं इसलिए \(a_5=37\) है। हर घटाव को क्रम से लिखें। / The subtracted values are (3,6,12,32), so \(a_5=37\). Exam tip: write each subtraction in order.

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Question 13/151 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)

Explanation

Simple Explanation

\(a_2=10\) और \(a_3=37\) है। गुणा के बाद (n+1) घटाएँ। / \(a_2=10\) and \(a_3=37\). Exam tip: multiply first and then subtract (n+1).

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Question 14/151 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)

Explanation

Simple Explanation

\(a_3=19\) और \(a_4=47\) है। दो-पद नियम में \(n^2\) भी जोड़ें। / \(a_3=19\) and \(a_4=47\). Exam tip: also add \(n^2\) in the two-term rule.

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Question 15/151 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)

Explanation

Simple Explanation

पद (5,11,23,47,95) हैं इसलिए \(a_5=95\) है। गुणा और घटाव का क्रम सही रखें। / The terms are (5,11,23,47,95), so \(a_5=95\). Exam tip: keep the order of multiplication and subtraction correct.

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Question 16/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (5,12,23) हैं इसलिए \(a_4=48\) है। गुणनफल और घात दोनों निकालें। / The added values are (5,12,23), so \(a_4=48\). Exam tip: calculate both the product and the power.

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Question 17/151 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)

Explanation

Simple Explanation

घटने वाले मान (5,12,23) हैं इसलिए \(a_4=140\) है। घटाने से पहले पूरा मान निकालें। / The subtracted values are (5,12,23), so \(a_4=140\). Exam tip: calculate the full value before subtracting.

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Question 18/151 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)

Explanation

Simple Explanation

पद (9,19,42) हैं इसलिए \(a_3=42\) है। पहले पिछले पद को दोगुना करें फिर (3n-2) जोड़ें। / The terms are (9,19,42), so \(a_3=42\). Exam tip: double the previous term first and then add (3n-2).

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Question 19/151 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)

Explanation

Simple Explanation

\(a_2=12\) और \(a_3=12\) है। भाग के बाद \(2n^2\) जोड़ें। / \(a_2=12\) and \(a_3=12\). Exam tip: divide first and then add \(2n^2\).

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Question 20/151 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)

Explanation

Simple Explanation

\(a_2=21\) और \(a_3=40\) है। \(a_1\) स्थिर रहता है जबकि \(n^2\) बदलता है। / \(a_2=21\) and \(a_3=40\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

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Question 21/151 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)

Explanation

Simple Explanation

पद (2,4,15,31,61) हैं इसलिए \(a_5=61\) है। पिछले दो पदों के साथ वर्तमान (3n) जोड़ें। / The terms are (2,4,15,31,61), so \(a_5=61\). Exam tip: add current (3n) with the previous two terms.

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Question 22/151 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)

Explanation

Simple Explanation

\(a_3=21\) और \(a_4=63\) है। गुणांक लगाने के बाद \(n^2\) भी जोड़ें। / \(a_3=21\) and \(a_4=63\). Exam tip: after applying coefficients, also add \(n^2\).

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Question 23/151 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)

Explanation

Simple Explanation

\(a_2=7\) और \(a_3=39\) है। वर्ग निकालकर \(2a_n\) घटाएँ और (4) जोड़ें। / \(a_2=7\) and \(a_3=39\). Exam tip: square, subtract \(2a_n\), and add (4).

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Question 24/151 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)

Explanation

Simple Explanation

\(a_2=4^2-4+2=14\) है। वर्ग लेकर वही पद घटाएँ और (2) जोड़ें। / \(a_2=4^2-4+2=14\). Exam tip: square the term, subtract it, and add (2).

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Question 25/151 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

Explanation

Simple Explanation

(79-13=66) और \(66\div6=11\) चरण हैं इसलिए पद संख्या (12) है। चरणों में (1) जोड़कर पद संख्या मिलती है। / (79-13=66), and \(66\div6=11\) steps, so the term number is (12). Exam tip: add (1) to the number of steps.

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Question 26/151 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)

Explanation

Simple Explanation

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

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Question 27/151 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)

Explanation

Simple Explanation

पद (4,17,43,95) हैं इसलिए \(a_4-a_2=78\) है। पहले दोनों पद निकालें फिर घटाएँ। / The terms are (4,17,43,95), so \(a_4-a_2=78\). Exam tip: find both terms first and then subtract.

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Question 28/151 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)

Explanation

Simple Explanation

पद (3,9,19,35,61) हैं इसलिए \(a_5=61\) है। पिछले दो पदों के साथ (7) भी जोड़ें। / The terms are (3,9,19,35,61), so \(a_5=61\). Exam tip: also add (7) with the previous two terms.

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Question 29/151 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)

Explanation

Simple Explanation

\(a_2=10\) और \(a_3=66\) है। पहले (7) से गुणा करें फिर (4) घटाएँ। / \(a_2=10\) and \(a_3=66\). Exam tip: multiply by (7) first and then subtract (4).

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Question 30/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (5,14,23) हैं इसलिए \(a_4=48\) है। (9n-4) का मान हर चरण में बदलता है। / The added values are (5,14,23), so \(a_4=48\). Exam tip: (9n-4) changes at each step.

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Question 31/151 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)

Explanation

Simple Explanation

घटने वाले मान (13,20,27) हैं इसलिए \(a_4=150\) है। घटाने से पहले (7n+6) निकालें। / The subtracted values are (13,20,27), so \(a_4=150\). Exam tip: calculate (7n+6) before subtracting.

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Question 32/151 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)

Explanation

Simple Explanation

\(a_3=10\) और \(a_4=41\) है। दोनों पिछले पदों के गुणांक सावधानी से लगाएँ। / \(a_3=10\) and \(a_4=41\). Exam tip: apply the coefficients of both previous terms carefully.

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Question 33/151 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)

Explanation

Simple Explanation

कुल जोड़ (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=42\) है। भिन्न जोड़ में कुल जोड़ पहले निकालें। / The total addition is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=42\). Exam tip: find total fractional addition first.

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Question 34/151 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)

Explanation

Simple Explanation

कुल घटाव (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=45\) है। भिन्न घटावों को पहले जोड़ें। / The total subtraction is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=45\). Exam tip: add fractional subtractions first.

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Question 35/151 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)

Explanation

Simple Explanation

\(a_2=9\), \(a_3=23\) और \(a_4=74\) है। गुणक (n) हर चरण में बदलता है। / \(a_2=9\), \(a_3=23\), and \(a_4=74\). Exam tip: the multiplier (n) changes at each step.

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Question 36/151 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)

Explanation

Simple Explanation

\(a_2=14\), \(a_3=55\) और \(a_4=274\) है। गुणक (n+2) बदलता है। / \(a_2=14\), \(a_3=55\), and \(a_4=274\). Exam tip: the multiplier (n+2) changes.

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Question 37/151 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. \(a_1=4, a_{n+1}=3a_n+2\)

Explanation

Simple Explanation

\(3\times4+2=14\) और \(3\times14+2=44\) है। नियम चुनते समय पहला पद भी जाँचें। / \(3\times4+2=14\) and \(3\times14+2=44\). Exam tip: check the first term too when selecting a rule.

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Question 38/151 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. \(a_1=6, a_{n+1}=a_n+3n+2\)

Explanation

Simple Explanation

जोड़ (5,8,11) हैं इसलिए (3n+2) जुड़ता है। पहला पद और बदलते जोड़ दोनों मिलाएँ। / The additions are (5,8,11), so (3n+2) is added. Exam tip: match both the first term and changing additions.

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Question 39/151 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

Explanation

Simple Explanation

पद (5,6,10,19,35,60) हैं इसलिए (60) छठा पद है। वर्ग जोड़ते समय क्रमांक साथ लिखें। / The terms are (5,6,10,19,35,60), so (60) is the sixth term. Exam tip: write positions while adding squares.

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Question 40/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (3,6,14,40) हैं इसलिए \(a_5=68\) है। फैक्टोरियल और घात दोनों निकालें। / The added values are (3,6,14,40), so \(a_5=68\). Exam tip: calculate both the factorial and the power.

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Question 41/151 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)

Explanation

Simple Explanation

घटने वाले मान (3,6,14,40) हैं इसलिए \(a_5=57\) है। पूरे घटावों का योग पहले निकालें। / The subtracted values are (3,6,14,40), so \(a_5=57\). Exam tip: find the sum of all subtractions first.

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Question 42/151 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)

Explanation

Simple Explanation

पद (4,5,15,23) हैं इसलिए \(a_4=23\) है। दोगुना करने के बाद चिह्न वाला भाग जोड़ें। / The terms are (4,5,15,23), so \(a_4=23\). Exam tip: double first and then add the signed part.

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Question 43/151 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)

Explanation

Simple Explanation

पद (50,52,47,57) हैं इसलिए \(a_4=57\) है। बाहरी ऋण और ((-1)^n) को साथ में देखें। / The terms are (50,52,47,57), so \(a_4=57\). Exam tip: track the outside minus sign with ((-1)^n).

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Question 44/151 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)

Explanation

Simple Explanation

पद (2,5,18,49,126) हैं इसलिए \(a_5=126\) है। वर्तमान (2n) को हर चरण में जोड़ें। / The terms are (2,5,18,49,126), so \(a_5=126\). Exam tip: add the current (2n) at each step.

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Question 45/151 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)

Explanation

Simple Explanation

पद (6,14,26,44) हैं इसलिए \(a_4=44\) है। \(a_1\) स्थिर है और (n(n+1)) बदलता है। / The terms are (6,14,26,44), so \(a_4=44\). Exam tip: \(a_1\) is fixed while (n(n+1)) changes.

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Question 46/151 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)

Explanation

Simple Explanation

जुड़ने वाले मान (9,25,49) हैं इसलिए \(a_4=86\) है। विषम वर्गों को क्रम से जोड़ें। / The added values are (9,25,49), so \(a_4=86\). Exam tip: add the odd squares in order.

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Question 47/151 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)

Explanation

Simple Explanation

घटने वाले वर्ग (9,25,49) हैं इसलिए \(a_4=97\) है। पहले वर्गों का योग निकालना आसान है। / The subtracted squares are (9,25,49), so \(a_4=97\). Exam tip: finding the sum of squares first is easier.

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Question 48/151 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)

Explanation

Simple Explanation

घन जोड़ (1,8,27,64) हैं इसलिए \(a_5=103\) है। हर चरण में \(n^3\) का नया मान जोड़ें। / The cube additions are (1,8,27,64), so \(a_5=103\). Exam tip: add the new value of \(n^3\) at each step.

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Question 49/151 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)

Explanation

Simple Explanation

घटने वाले घन (1,8,27,64) हैं इसलिए \(a_5=50\) है। घनों का योग पहले निकालें। / The subtracted cubes are (1,8,27,64), so \(a_5=50\). Exam tip: find the sum of cubes first.

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Question 50/151 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. \(a_1=3, a_2=8, a_n=2a_{n-1}+a_{n-2}\)

Explanation

Simple Explanation

\(2\times8+3=19\) और \(2\times19+8=46\) है। दो-पद नियम में दोनों शुरुआती पद सही होने चाहिए। / \(2\times8+3=19\) and \(2\times19+8=46\). Exam tip: both starting terms must be correct in a two-term rule.

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Question 51/151 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)

Explanation

Simple Explanation

\(a_3=21\) और \(a_4=43\) है। \(a_{n-2}\) को (3) से गुणा करके वर्तमान (n) जोड़ें। / \(a_3=21\) and \(a_4=43\). Exam tip: multiply \(a_{n-2}\) by (3) and add current (n).

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Question 52/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

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

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

Explanation opens after your attempt
Correct Answer

C. उनचास(49)

Explanation

Simple Explanation

\(a_2=9\), \(a_3=22\) और \(a_4=49\) मिलता है। परीक्षा में (n) का वर्तमान मान सही रखें। / We get \(a_2=9\), \(a_3=22\), and \(a_4=49\). In exams, keep the current value of (n) correct.

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Question 53/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(b_1=6\) और \(b_n=3b_{n-1}-n\) है। \(b_4\) का मान क्या होगा?

In a sequence, \(b_1=6\) and \(b_n=3b_{n-1}-n\). What is the value of \(b_4\)?

Explanation opens after your attempt
Correct Answer

B. एक सौ इकतीस(131)

Explanation

Simple Explanation

\(b_2=16\), \(b_3=45\) और \(b_4=131\) मिलता है। परीक्षा में गुणा और घटाव दोनों ध्यान से करें। / We get \(b_2=16\), \(b_3=45\), and \(b_4=131\). In exams, handle both multiplication and subtraction carefully.

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Question 54/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(c_1=1\), \(c_2=3\) और \(c_n=2c_{n-1}+c_{n-2}\) है। \(c_5\) का मान क्या होगा?

In a sequence, \(c_1=1\), \(c_2=3\), and \(c_n=2c_{n-1}+c_{n-2}\). What is the value of \(c_5\)?

Explanation opens after your attempt
Correct Answer

D. इकतालीस(41)

Explanation

Simple Explanation

\(c_3=7\), \(c_4=17\) और \(c_5=41\) मिलता है। परीक्षा में पिछले दो पदों का क्रम न बदलें। / We get \(c_3=7\), \(c_4=17\), and \(c_5=41\). In exams, do not interchange the previous two terms.

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Question 55/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(d_n=d_{n-1}+2n\) और \(d_4=25\) है, तो \(d_1\) का मान क्या होगा?

If \(d_n=d_{n-1}+2n\) and \(d_4=25\), what is the value of \(d_1\)?

Explanation opens after your attempt
Correct Answer

A. सात(7)

Explanation

Simple Explanation

\(d_4=d_1+4+6+8\), इसलिए \(d_1=7\) है। परीक्षा में पीछे की ओर भी वही नियम लागू करें। / \(d_4=d_1+4+6+8\), so \(d_1=7\). In exams, apply the same rule backward too.

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Question 56/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम (4), (9), (19), (39) के लिए कौन-सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence (4), (9), (19), (39)?

Explanation opens after your attempt
Correct Answer

B. नियम \(e_n=2e_{n-1}+1\)Rule \(e_n=2e_{n-1}+1\)

Explanation

Simple Explanation

हर नया पद पिछले पद के दोगुने में (1) जोड़ने से मिलता है। परीक्षा में नियम को दो पदों पर जाँचें। / Each new term is obtained by doubling the previous term and adding (1). In exams, test the rule on two terms.

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Question 57/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(f_1=10\) और \(f_n=f_{n-1}-n\) है, तो पहला ऋणात्मक पद कौन-सा होगा?

If \(f_1=10\) and \(f_n=f_{n-1}-n\), which will be the first negative term?

Explanation opens after your attempt
Correct Answer

D. पाँचवाँ पद(5)

Explanation

Simple Explanation

\(f_2=8\), \(f_3=5\), \(f_4=1\) और \(f_5=-4\) है। परीक्षा में शून्य से नीचे जाने वाला पहला पद देखें। / \(f_2=8\), \(f_3=5\), \(f_4=1\), and \(f_5=-4\). In exams, find the first term that goes below zero.

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Question 58/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(g_1=2\) और \(g_n=g_{n-1}+2n-1\) है। \(g_5\) का मान क्या होगा?

In a sequence, \(g_1=2\) and \(g_n=g_{n-1}+2n-1\). What is the value of \(g_5\)?

Explanation opens after your attempt
Correct Answer

A. छब्बीस(26)

Explanation

Simple Explanation

क्रमशः (3), (5), (7), (9) जोड़ने पर \(g_5=26\) मिलता है। परीक्षा में जोड़ी गई राशियों को अलग लिखें। / Adding (3), (5), (7), and (9) gives \(g_5=26\). In exams, write the added quantities separately.

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Question 59/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(h_1=3\) और \(h_n=n h_{n-1}\) है, तो \(h_4\) का मान क्या होगा?

If \(h_1=3\) and \(h_n=n h_{n-1}\), what is the value of \(h_4\)?

Explanation opens after your attempt
Correct Answer

C. बहत्तर(72)

Explanation

Simple Explanation

\(h_2=6\), \(h_3=18\) और \(h_4=72\) होता है। परीक्षा में हर चरण में (n) से गुणा करें। / \(h_2=6\), \(h_3=18\), and \(h_4=72\). In exams, multiply by (n) at each step.

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Question 60/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(j_1=1\) और \(j_n=j_{n-1}+n^2\) है। \(j_4\) का मान क्या होगा?

In a sequence, \(j_1=1\) and \(j_n=j_{n-1}+n^2\). What is the value of \(j_4\)?

Explanation opens after your attempt
Correct Answer

B. तीस(30)

Explanation

Simple Explanation

\(j_4=1+4+9+16=30\) है। परीक्षा में \(n^2\) का मान पहले निकालें। / \(j_4=1+4+9+16=30\). In exams, calculate \(n^2\) first.

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Question 61/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(k_1=64\) और \(k_n=\frac{k_{n-1}}{2}+n\) है, तो \(k_4\) का मान क्या होगा?

If \(k_1=64\) and \(k_n=\frac{k_{n-1}}{2}+n\), what is the value of \(k_4\)?

Explanation opens after your attempt
Correct Answer

D. चौदह(14)

Explanation

Simple Explanation

\(k_2=34\), \(k_3=20\) और \(k_4=14\) मिलता है। परीक्षा में भाग देने के बाद (n) जोड़ें। / \(k_2=34\), \(k_3=20\), and \(k_4=14\). In exams, add (n) after dividing.

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Question 62/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(m_1=2\) और \(m_n=m_{n-1}+3n\) है। \(m_4\) का मान क्या होगा?

In a sequence, \(m_1=2\) and \(m_n=m_{n-1}+3n\). What is the value of \(m_4\)?

Explanation opens after your attempt
Correct Answer

A. उनतीस(29)

Explanation

Simple Explanation

\(m_4=2+6+9+12=29\) है। परीक्षा में जोड़ (n=2) से शुरू करें। / \(m_4=2+6+9+12=29\). In exams, start adding from (n=2).

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Question 63/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(n_1=5\) और \(n_n=2n_{n-1}-n^2\) है, तो \(n_4\) का मान क्या होगा?

If \(n_1=5\) and \(n_n=2n_{n-1}-n^2\), what is the value of \(n_4\)?

Explanation opens after your attempt
Correct Answer

C. ऋण दस(-10)

Explanation

Simple Explanation

\(n_2=6\), \(n_3=3\) और \(n_4=-10\) है। परीक्षा में ऋणात्मक उत्तर आने पर भी गणना न छोड़ें। / \(n_2=6\), \(n_3=3\), and \(n_4=-10\). In exams, do not stop the calculation when a negative answer appears.

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Question 64/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(r_1=1\), \(r_2=2\) और \(r_n=r_{n-1}+3r_{n-2}\) है, तो \(r_5\) का मान क्या होगा?

If \(r_1=1\), \(r_2=2\), and \(r_n=r_{n-1}+3r_{n-2}\), what is the value of \(r_5\)?

Explanation opens after your attempt
Correct Answer

B. छब्बीस(26)

Explanation

Simple Explanation

\(r_3=5\), \(r_4=11\) और \(r_5=26\) मिलता है। परीक्षा में दूसरे पिछले पद को (3) से गुणा करें। / \(r_3=5\), \(r_4=11\), and \(r_5=26\). In exams, multiply the second previous term by (3).

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Question 65/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(s_1=3\) और (s_n=s_{n-1}+(-1)^n n) है। \(s_5\) का मान क्या होगा?

In a sequence, \(s_1=3\) and (s_n=s_{n-1}+(-1)^n n). What is the value of \(s_5\)?

Explanation opens after your attempt
Correct Answer

D. एक(1)

Explanation

Simple Explanation

\(s_2=5\), \(s_3=2\), \(s_4=6\) और \(s_5=1\) है। परीक्षा में चिह्न बदलने वाले नियम को सावधानी से पढ़ें। / \(s_2=5\), \(s_3=2\), \(s_4=6\), and \(s_5=1\). In exams, read alternating-sign rules carefully.

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Question 66/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(t_1=x\), \(t_n=t_{n-1}+n\) और \(t_5=24\) है, तो (x) का मान क्या होगा?

If \(t_1=x\), \(t_n=t_{n-1}+n\), and \(t_5=24\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

A. दस(10)

Explanation

Simple Explanation

\(t_5=x+2+3+4+5\), इसलिए (x=10) है। परीक्षा में अज्ञात प्रथम पद को अलग रखें। / \(t_5=x+2+3+4+5\), so (x=10). In exams, keep the unknown first term separate.

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Question 67/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम (2), (6), (18), (54) के लिए सही पुनरावर्ती नियम कौन-सा है?

Which recursive rule is correct for the sequence (2), (6), (18), (54)?

Explanation opens after your attempt
Correct Answer

C. नियम \(a_n=3a_{n-1}\)Rule \(a_n=3a_{n-1}\)

Explanation

Simple Explanation

हर पद पिछले पद का (3) गुना है। परीक्षा में लगातार अनुपात देखकर नियम पहचानें। / Each term is (3) times the previous term. In exams, identify the rule by checking consecutive ratios.

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Question 68/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(v_1=4\) और \(v_n=2v_{n-1}-1\) है, तो \(v_5\) का मान क्या होगा?

If \(v_1=4\) and \(v_n=2v_{n-1}-1\), what is the value of \(v_5\)?

Explanation opens after your attempt
Correct Answer

D. उनचास(49)

Explanation

Simple Explanation

\(v_2=7\), \(v_3=13\), \(v_4=25\) और \(v_5=49\) है। परीक्षा में पहले दोगुना करें फिर (1) घटाएँ। / \(v_2=7\), \(v_3=13\), \(v_4=25\), and \(v_5=49\). In exams, double first and then subtract (1).

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Question 69/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(w_1=0\) और \(w_n=w_{n-1}+2^{n-1}\) है। \(w_5\) का मान क्या होगा?

In a sequence, \(w_1=0\) and \(w_n=w_{n-1}+2^{n-1}\). What is the value of \(w_5\)?

Explanation opens after your attempt
Correct Answer

B. तीस(30)

Explanation

Simple Explanation

\(w_5=0+2+4+8+16=30\) है। परीक्षा में घात (n-1) को सही लगाएँ। / \(w_5=0+2+4+8+16=30\). In exams, apply the exponent (n-1) correctly.

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Question 70/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(x_1=1\) और \(x_n=2x_{n-1}+n^2\) है, तो \(x_3\) का मान क्या होगा?

If \(x_1=1\) and \(x_n=2x_{n-1}+n^2\), what is the value of \(x_3\)?

Explanation opens after your attempt
Correct Answer

C. इक्कीस(21)

Explanation

Simple Explanation

\(x_2=6\) और \(x_3=21\) मिलता है। परीक्षा में वर्ग जोड़ने से पहले पिछले पद को दोगुना करें। / \(x_2=6\) and \(x_3=21\). In exams, double the previous term before adding the square.

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Question 71/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(y_1=7\) और (y_n=y_{n-1}+(n-1)2) है। \(y_5\) का मान क्या होगा?

In a sequence, \(y_1=7\) and (y_n=y_{n-1}+(n-1)2). What is the value of \(y_5\)?

Explanation opens after your attempt
Correct Answer

A. सैंतीस(37)

Explanation

Simple Explanation

\(y_5=7+1+4+9+16=37\) है। परीक्षा में (n-1) का वर्ग लेना न भूलें। / \(y_5=7+1+4+9+16=37\). In exams, remember to square (n-1).

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Question 72/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(z_1=2\), \(z_2=3\) और \(z_n=z_{n-1}z_{n-2}+1\) है, तो \(z_5\) का मान क्या होगा?

If \(z_1=2\), \(z_2=3\), and \(z_n=z_{n-1}z_{n-2}+1\), what is the value of \(z_5\)?

Explanation opens after your attempt
Correct Answer

D. एक सौ पचपन(155)

Explanation

Simple Explanation

\(z_3=7\), \(z_4=22\) और \(z_5=155\) मिलता है। परीक्षा में पिछले दो पदों का गुणन सही करें। / \(z_3=7\), \(z_4=22\), and \(z_5=155\). In exams, multiply the two previous terms carefully.

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Question 73/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(A_1=1\) और \(A_n=nA_{n-1}+1\) है। \(A_4\) का मान क्या होगा?

In a sequence, \(A_1=1\) and \(A_n=nA_{n-1}+1\). What is the value of \(A_4\)?

Explanation opens after your attempt
Correct Answer

B. इकतालीस(41)

Explanation

Simple Explanation

\(A_2=3\), \(A_3=10\) और \(A_4=41\) है। परीक्षा में (n) से गुणा करके (1) जोड़ें। / \(A_2=3\), \(A_3=10\), and \(A_4=41\). In exams, multiply by (n) and then add (1).

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Question 74/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(B_1=9\) और \(B_n=B_{n-1}+2^n\) है, तो \(B_4\) का मान क्या होगा?

If \(B_1=9\) and \(B_n=B_{n-1}+2^n\), what is the value of \(B_4\)?

Explanation opens after your attempt
Correct Answer

C. सैंतीस(37)

Explanation

Simple Explanation

\(B_4=9+4+8+16=37\) है। परीक्षा में जोड़ (n=2) से शुरू होता है। / \(B_4=9+4+8+16=37\). In exams, the addition starts from (n=2).

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Question 75/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(C_1=5\) और (C_n=C_{n-1}+n(n-1)) है। \(C_4\) का मान क्या होगा?

In a sequence, \(C_1=5\) and (C_n=C_{n-1}+n(n-1)). What is the value of \(C_4\)?

Explanation opens after your attempt
Correct Answer

A. पच्चीस(25)

Explanation

Simple Explanation

\(C_4=5+2+6+12=25\) है। परीक्षा में (n(n-1)) को पहले सरल करें। / \(C_4=5+2+6+12=25\). In exams, simplify (n(n-1)) first.

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Question 76/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(D_1=2\) और \(D_n=2D_{n-1}+n-1\) है, तो \(D_4\) का मान क्या होगा?

If \(D_1=2\) and \(D_n=2D_{n-1}+n-1\), what is the value of \(D_4\)?

Explanation opens after your attempt
Correct Answer

D. सत्ताईस(27)

Explanation

Simple Explanation

\(D_2=5\), \(D_3=12\) और \(D_4=27\) है। परीक्षा में (n-1) को अलग से जोड़ें। / \(D_2=5\), \(D_3=12\), and \(D_4=27\). In exams, add (n-1) separately.

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Question 77/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(E_1=1\), \(E_2=4\) और \(E_n=E_{n-1}+E_{n-2}+2\) है, तो \(E_5\) का मान क्या होगा?

If \(E_1=1\), \(E_2=4\), and \(E_n=E_{n-1}+E_{n-2}+2\), what is the value of \(E_5\)?

Explanation opens after your attempt
Correct Answer

C. बाईस(22)

Explanation

Simple Explanation

\(E_3=7\), \(E_4=13\) और \(E_5=22\) है। परीक्षा में दोनों पिछले पदों के बाद (2) जोड़ें। / \(E_3=7\), \(E_4=13\), and \(E_5=22\). In exams, add (2) after using both previous terms.

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Question 78/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(F_1=20\) और \(F_n=F_{n-1}-2n+1\) है। \(F_5\) का मान क्या होगा?

In a sequence, \(F_1=20\) and \(F_n=F_{n-1}-2n+1\). What is the value of \(F_5\)?

Explanation opens after your attempt
Correct Answer

B. ऋण चार(-4)

Explanation

Simple Explanation

\(F_2=17\), \(F_3=12\), \(F_4=5\) और \(F_5=-4\) है। परीक्षा में घटाई जाने वाली राशि (2n-1) समझें। / \(F_2=17\), \(F_3=12\), \(F_4=5\), and \(F_5=-4\). In exams, understand the subtracted amount as (2n-1).

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Question 79/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(G_1=3\) और \(G_n=n+2G_{n-1}\) है, तो \(G_4\) का मान क्या होगा?

If \(G_1=3\) and \(G_n=n+2G_{n-1}\), what is the value of \(G_4\)?

Explanation opens after your attempt
Correct Answer

A. बयालीस(42)

Explanation

Simple Explanation

\(G_2=8\), \(G_3=19\) और \(G_4=42\) है। परीक्षा में (n) जोड़ने से पहले पिछले पद को दोगुना करें। / \(G_2=8\), \(G_3=19\), and \(G_4=42\). In exams, double the previous term before adding (n).

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Question 80/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(H_1=2\) और (H_n=H_{n-1}+n(n+1)) है। \(H_4\) का मान क्या होगा?

In a sequence, \(H_1=2\) and (H_n=H_{n-1}+n(n+1)). What is the value of \(H_4\)?

Explanation opens after your attempt
Correct Answer

D. चालीस(40)

Explanation

Simple Explanation

\(H_4=2+6+12+20=40\) है। परीक्षा में (n(n+1)) को प्रत्येक चरण पर निकालें। / \(H_4=2+6+12+20=40\). In exams, calculate (n(n+1)) at each step.

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Question 81/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(J_1=50\) और (J_n=J_{n-1}-3(n-1)) है, तो \(J_5\) का मान क्या होगा?

If \(J_1=50\) and (J_n=J_{n-1}-3(n-1)), what is the value of \(J_5\)?

Explanation opens after your attempt
Correct Answer

C. बीस(20)

Explanation

Simple Explanation

\(J_5=50-3-6-9-12=20\) है। परीक्षा में घटाव (n=2) से शुरू करें। / \(J_5=50-3-6-9-12=20\). In exams, start the subtraction from (n=2).

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Question 82/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(K_1=1\), \(K_2=1\) और \(K_n=2K_{n-1}+K_{n-2}\) है, तो \(K_5\) का मान क्या होगा?

If \(K_1=1\), \(K_2=1\), and \(K_n=2K_{n-1}+K_{n-2}\), what is the value of \(K_5\)?

Explanation opens after your attempt
Correct Answer

B. सत्रह(17)

Explanation

Simple Explanation

\(K_3=3\), \(K_4=7\) और \(K_5=17\) है। परीक्षा में पिछले पद का दोगुना लेकर उससे पहले वाला पद जोड़ें। / \(K_3=3\), \(K_4=7\), and \(K_5=17\). In exams, double the previous term and add the term before it.

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Question 83/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(L_1=6\) और \(L_n=L_{n-1}+2n+1\) है। \(L_5\) का मान क्या होगा?

In a sequence, \(L_1=6\) and \(L_n=L_{n-1}+2n+1\). What is the value of \(L_5\)?

Explanation opens after your attempt
Correct Answer

A. अड़तीस(38)

Explanation

Simple Explanation

\(L_5=6+5+7+9+11=38\) है। परीक्षा में (2n+1) की विषम संख्याएँ सही जोड़ें। / \(L_5=6+5+7+9+11=38\). In exams, add the odd numbers from (2n+1) correctly.

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Question 84/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(M_1=1\) और \(M_n=3M_{n-1}+n\) है, तो \(M_3\) का मान क्या होगा?

If \(M_1=1\) and \(M_n=3M_{n-1}+n\), what is the value of \(M_3\)?

Explanation opens after your attempt
Correct Answer

D. अठारह(18)

Explanation

Simple Explanation

\(M_2=5\) और \(M_3=18\) है। परीक्षा में गुणा (3) के बाद (n) जोड़ें। / \(M_2=5\) and \(M_3=18\). In exams, add (n) after multiplying by (3).

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Question 85/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(R_1=2\) और \(R_n=nR_{n-1}+n\) है। \(R_4\) का मान क्या होगा?

In a sequence, \(R_1=2\) and \(R_n=nR_{n-1}+n\). What is the value of \(R_4\)?

Explanation opens after your attempt
Correct Answer

C. अठासी(88)

Explanation

Simple Explanation

\(R_2=6\), \(R_3=21\) और \(R_4=88\) है। परीक्षा में (n) से गुणा और (n) जोड़ना दोनों करें। / \(R_2=6\), \(R_3=21\), and \(R_4=88\). In exams, both multiply by (n) and add (n).

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Question 86/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(O_1=4\) और \(O_n=O_{n-1}+2^n+n\) है, तो \(O_4\) का मान क्या होगा?

If \(O_1=4\) and \(O_n=O_{n-1}+2^n+n\), what is the value of \(O_4\)?

Explanation opens after your attempt
Correct Answer

B. इकतालीस(41)

Explanation

Simple Explanation

\(O_2=10\), \(O_3=21\) और \(O_4=41\) है। परीक्षा में घात और (n) दोनों जोड़ें। / \(O_2=10\), \(O_3=21\), and \(O_4=41\). In exams, add both the power and (n).

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Question 87/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(P_1=3\) और \(P_n=P_{n-1}+4n-3\) है। \(P_5\) का मान क्या होगा?

In a sequence, \(P_1=3\) and \(P_n=P_{n-1}+4n-3\). What is the value of \(P_5\)?

Explanation opens after your attempt
Correct Answer

D. सैंतालीस(47)

Explanation

Simple Explanation

\(P_5=3+5+9+13+17=47\) है। परीक्षा में (4n-3) से बनने वाली संख्याएँ क्रम से जोड़ें। / \(P_5=3+5+9+13+17=47\). In exams, add the numbers formed by (4n-3) in order.

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Question 88/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(Q_1=2\), \(Q_2=5\) और \(Q_n=Q_{n-1}+2Q_{n-2}+n\) है, तो \(Q_5\) का मान क्या होगा?

If \(Q_1=2\), \(Q_2=5\), and \(Q_n=Q_{n-1}+2Q_{n-2}+n\), what is the value of \(Q_5\)?

Explanation opens after your attempt
Correct Answer

A. पचपन(55)

Explanation

Simple Explanation

\(Q_3=12\), \(Q_4=26\) और \(Q_5=55\) है। परीक्षा में दूसरे पिछले पद को दोगुना करना न भूलें। / \(Q_3=12\), \(Q_4=26\), and \(Q_5=55\). In exams, do not forget to double the second previous term.

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Question 89/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(R_1=1\) और \(R_n=R_{n-1}^2+n\) है, तो \(R_3\) का मान क्या होगा?

If \(R_1=1\) and \(R_n=R_{n-1}^2+n\), what is the value of \(R_3\)?

Explanation opens after your attempt
Correct Answer

C. बारह(12)

Explanation

Simple Explanation

\(R_2=3\) और \(R_3=12\) है। परीक्षा में पिछले पद का वर्ग लेने के बाद (n) जोड़ें। / \(R_2=3\) and \(R_3=12\). In exams, square the previous term and then add (n).

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Question 90/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(S_1=100\) और \(S_n=S_{n-1}-n^2\) है। \(S_4\) का मान क्या होगा?

In a sequence, \(S_1=100\) and \(S_n=S_{n-1}-n^2\). What is the value of \(S_4\)?

Explanation opens after your attempt
Correct Answer

B. इकहत्तर(71)

Explanation

Simple Explanation

\(S_4=100-4-9-16=71\) है। परीक्षा में \(n^2\) को घटाना है, जोड़ना नहीं। / \(S_4=100-4-9-16=71\). In exams, subtract \(n^2\), do not add it.

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Question 91/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(T_1=2\) और (T_n=(n+1)T_{n-1}-n) है, तो \(T_4\) का मान क्या होगा?

If \(T_1=2\) and (T_n=(n+1)T_{n-1}-n), what is the value of \(T_4\)?

Explanation opens after your attempt
Correct Answer

D. इकसठ(61)

Explanation

Simple Explanation

\(T_2=4\), \(T_3=13\) और \(T_4=61\) है। परीक्षा में ((n+1)) से गुणा करके (n) घटाएँ। / \(T_2=4\), \(T_3=13\), and \(T_4=61\). In exams, multiply by ((n+1)) and subtract (n).

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Question 92/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम के पहले चार पद (5), (8), (14), (26) हैं और नियम \(a_n=2a_{n-1}-2\) है। \(a_5\) क्या होगा?

The first four terms of a sequence are (5), (8), (14), (26), and the rule is \(a_n=2a_{n-1}-2\). What is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. पचास(50)

Explanation

Simple Explanation

\(a_5=2\times 26-2=50\) है। परीक्षा में दिए अंतिम पद पर नियम लगाएँ। / \(a_5=2\times 26-2=50\). In exams, apply the rule to the last given term.

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Question 93/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_n=a_{n-1}+3n\) और \(a_4=31\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=a_{n-1}+3n\) and \(a_4=31\), what is the value of \(a_2\)?

Explanation opens after your attempt
Correct Answer

A. दस(10)

Explanation

Simple Explanation

\(a_4=a_2+9+12\), इसलिए \(a_2=10\) है। परीक्षा में बीच के पद के लिए उल्टी दिशा में सोचें। / \(a_4=a_2+9+12\), so \(a_2=10\). In exams, think backward for a middle term.

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Question 94/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(b_n=2b_{n-1}+n\) और \(b_3=19\) है, तो \(b_1\) का मान क्या होगा?

If \(b_n=2b_{n-1}+n\) and \(b_3=19\), what is the value of \(b_1\)?

Explanation opens after your attempt
Correct Answer

B. तीन(3)

Explanation

Simple Explanation

\(b_3=4b_1+7\), इसलिए \(b_1=3\) है। परीक्षा में पुनरावर्ती नियम को प्रथम पद तक फैलाएँ। / \(b_3=4b_1+7\), so \(b_1=3\). In exams, expand the recursive rule up to the first term.

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Question 95/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(c_1=2\) और \(c_n=c_{n-1}+n^2\) है, तो कौन-सा कथन सही है?

If \(c_1=2\) and \(c_n=c_{n-1}+n^2\), which statement is correct?

Explanation opens after your attempt
Correct Answer

D. \(c_2=6\) और \(c_3=15\)\(c_2=6\) and \(c_3=15\)

Explanation

Simple Explanation

\(c_2=2+4=6\) और \(c_3=6+9=15\) है। परीक्षा में प्रत्येक पद के लिए नया वर्ग जोड़ें। / \(c_2=2+4=6\) and \(c_3=6+9=15\). In exams, add the new square for each term.

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Question 96/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(d_1=1\) और \(d_n=d_{n-1}+3n\) है, तो \(d_n>40\) पहली बार किस (n) पर होगा?

If \(d_1=1\) and \(d_n=d_{n-1}+3n\), for which (n) will \(d_n>40\) first occur?

Explanation opens after your attempt
Correct Answer

C. पाँच(5)

Explanation

Simple Explanation

\(d_4=28\) और \(d_5=43\), इसलिए पहली बार (n=5) पर शर्त पूरी होती है। परीक्षा में सीमा पार करने वाला पहला पद चुनें। / \(d_4=28\) and \(d_5=43\), so the condition is first satisfied at (n=5). In exams, choose the first term that crosses the limit.

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Question 97/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(e_1=3\) और \(e_n=2e_{n-1}+n\) है, तो \(e_5-e_4\) का मान क्या होगा?

If \(e_1=3\) and \(e_n=2e_{n-1}+n\), what is the value of \(e_5-e_4\)?

Explanation opens after your attempt
Correct Answer

A. सैंतालीस(47)

Explanation

Simple Explanation

\(e_4=42\) और \(e_5=89\), इसलिए अंतर (47) है। परीक्षा में पहले दोनों पद अलग-अलग निकालें। / \(e_4=42\) and \(e_5=89\), so the difference is (47). In exams, find both terms separately first.

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Question 98/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(f_1=2\) और \(f_n=f_{n-1}+2n\) है, तो पहले चार पदों का योग क्या होगा?

If \(f_1=2\) and \(f_n=f_{n-1}+2n\), what is the sum of the first four terms?

Explanation opens after your attempt
Correct Answer

D. चालीस(40)

Explanation

Simple Explanation

पहले चार पद (2), (6), (12), (20) हैं और योग (40) है। परीक्षा में योग पूछने पर सभी पद जोड़ें। / The first four terms are (2), (6), (12), and (20), and their sum is (40). In exams, add all terms when the sum is asked.

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Question 99/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(g_1=1\) और \(g_n=3g_{n-1}-1\) है, तो \(g_4:g_3\) क्या होगा?

If \(g_1=1\) and \(g_n=3g_{n-1}-1\), what is \(g_4:g_3\)?

Explanation opens after your attempt
Correct Answer

B. (14:5)

Explanation

Simple Explanation

\(g_3=5\) और \(g_4=14\), इसलिए अनुपात (14:5) है। परीक्षा में अनुपात का क्रम न बदलें। / \(g_3=5\) and \(g_4=14\), so the ratio is (14:5). In exams, do not reverse the order of a ratio.

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Question 100/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(h_1=2\), \(h_2=7\) और \(h_n=2h_{n-1}-h_{n-2}+3\) है, तो \(h_5\) का मान क्या होगा?

If \(h_1=2\), \(h_2=7\), and \(h_n=2h_{n-1}-h_{n-2}+3\), what is the value of \(h_5\)?

Explanation opens after your attempt
Correct Answer

C. चालीस(40)

Explanation

Simple Explanation

\(h_3=15\), \(h_4=26\) और \(h_5=40\) है। परीक्षा में घटाए जाने वाले पद को सही पहचानें। / \(h_3=15\), \(h_4=26\), and \(h_5=40\). In exams, identify the term being subtracted correctly.

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Question 101/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(p_1=1\) और \(p_n=p_{n-1}+n^2-n\) है, तो \(p_5\) का मान क्या होगा?

If \(p_1=1\) and \(p_n=p_{n-1}+n^2-n\), what is the value of \(p_5\)?

Explanation opens after your attempt
Correct Answer

A. इकतालीस(41)

Explanation

Simple Explanation

\(p_5=1+2+6+12+20=41\) है। परीक्षा में \(n^2-n\) को सरल करके जोड़ें। / \(p_5=1+2+6+12+20=41\). In exams, simplify \(n^2-n\) and then add.

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Question 102/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(a_1=4\) और \(a_n=2a_{n-1}+n+2\) है। \(a_5\) का मान क्या होगा?

In a sequence, \(a_1=4\) and \(a_n=2a_{n-1}+n+2\). What is the value of \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. एक सौ पैंतीस(135)

Explanation

Simple Explanation

\(a_2=12\), \(a_3=29\), \(a_4=64\) और \(a_5=135\) मिलता है। परीक्षा में (n) का वर्तमान मान सही जोड़ें। / \(a_2=12\), \(a_3=29\), \(a_4=64\), and \(a_5=135\). In exams, add the current value of (n) correctly.

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Question 103/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(b_1=7\) और \(b_n=3b_{n-1}-2n+1\) है। \(b_4\) का मान क्या होगा?

In a sequence, \(b_1=7\) and \(b_n=3b_{n-1}-2n+1\). What is the value of \(b_4\)?

Explanation opens after your attempt
Correct Answer

B. एक सौ चालीस(140)

Explanation

Simple Explanation

\(b_2=18\), \(b_3=49\) और \(b_4=140\) है। परीक्षा में गुणा के बाद पूरी घटाई गई राशि जाँचें। / \(b_2=18\), \(b_3=49\), and \(b_4=140\). In exams, check the full subtracted amount after multiplication.

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Question 104/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(c_1=2\), \(c_2=5\) और \(c_n=c_{n-1}+2c_{n-2}+n\) है, तो \(c_5\) का मान क्या होगा?

If \(c_1=2\), \(c_2=5\), and \(c_n=c_{n-1}+2c_{n-2}+n\), what is the value of \(c_5\)?

Explanation opens after your attempt
Correct Answer

D. पचपन(55)

Explanation

Simple Explanation

\(c_3=12\), \(c_4=26\) और \(c_5=55\) मिलता है। परीक्षा में दूसरे पिछले पद को (2) से गुणा करें। / \(c_3=12\), \(c_4=26\), and \(c_5=55\). In exams, multiply the second previous term by (2).

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Question 105/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(d_n=d_{n-1}+5n-1\) और \(d_5=79\) है, तो \(d_1\) का मान क्या होगा?

If \(d_n=d_{n-1}+5n-1\) and \(d_5=79\), what is the value of \(d_1\)?

Explanation opens after your attempt
Correct Answer

A. तेरह(13)

Explanation

Simple Explanation

\(d_5=d_1+9+14+19+24\), इसलिए \(d_1=13\) है। परीक्षा में उल्टी दिशा में जोड़ी गई राशियाँ घटाएँ। / \(d_5=d_1+9+14+19+24\), so \(d_1=13\). In exams, subtract the added quantities when working backward.

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Question 106/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

अनुक्रम (6), (14), (30), (62) के लिए सही पुनरावर्ती नियम कौन-सा है?

Which recursive rule is correct for the sequence (6), (14), (30), (62)?

Explanation opens after your attempt
Correct Answer

D. नियम \(u_n=2u_{n-1}+2\)Rule \(u_n=2u_{n-1}+2\)

Explanation

Simple Explanation

हर नया पद पिछले पद के दोगुने में (2) जोड़ने से मिलता है। परीक्षा में नियम को लगातार दो जगह जाँचें। / Each new term is obtained by doubling the previous term and adding (2). In exams, test the rule at two consecutive places.

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Question 107/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(f_1=4\) और \(f_n=2f_{n-1}+3\) है, तो \(f_n>150\) पहली बार किस (n) पर होगा?

If \(f_1=4\) and \(f_n=2f_{n-1}+3\), for which (n) will \(f_n>150\) first occur?

Explanation opens after your attempt
Correct Answer

C. छह(6)

Explanation

Simple Explanation

\(f_5=109\) और \(f_6=221\), इसलिए पहली बार (n=6) पर शर्त पूरी होती है। परीक्षा में सीमा पार करने वाला पहला पद चुनें। / \(f_5=109\) and \(f_6=221\), so the condition is first satisfied at (n=6). In exams, choose the first term that crosses the limit.

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Question 108/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(g_1=10\) और (g_n=g_{n-1}+(-1)^n n-2) है। \(g_5\) का मान क्या होगा?

In a sequence, \(g_1=10\) and (g_n=g_{n-1}+(-1)^n n-2). What is the value of \(g_5\)?

Explanation opens after your attempt
Correct Answer

C. ऋण चार(-4)

Explanation

Simple Explanation

\(g_2=14\), \(g_3=5\), \(g_4=21\) और \(g_5=-4\) है। परीक्षा में बदलते हुए चिह्न को सावधानी से लगाएँ। / \(g_2=14\), \(g_3=5\), \(g_4=21\), and \(g_5=-4\). In exams, apply the alternating sign carefully.

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Question 109/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(h_1=2\) और (h_n=(n-1)h_{n-1}+3) है, तो \(h_4\) का मान क्या होगा?

If \(h_1=2\) and (h_n=(n-1)h_{n-1}+3), what is the value of \(h_4\)?

Explanation opens after your attempt
Correct Answer

A. बयालीस(42)

Explanation

Simple Explanation

\(h_2=5\), \(h_3=13\) और \(h_4=42\) होता है। परीक्षा में गुणक (n-1) को सही पहचानें। / \(h_2=5\), \(h_3=13\), and \(h_4=42\). In exams, identify the multiplier (n-1) correctly.

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Question 110/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(j_1=3\) और \(j_n=j_{n-1}+n^2+n\) है। \(j_4\) का मान क्या होगा?

In a sequence, \(j_1=3\) and \(j_n=j_{n-1}+n^2+n\). What is the value of \(j_4\)?

Explanation opens after your attempt
Correct Answer

B. इकतालीस(41)

Explanation

Simple Explanation

\(j_4=3+6+12+20=41\) है। परीक्षा में \(n^2+n\) को पहले सरल करें। / \(j_4=3+6+12+20=41\). In exams, simplify \(n^2+n\) first.

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Question 111/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(k_1=80\) और \(k_n=\frac{k_{n-1}}{2}+n\) है, तो \(k_5\) का मान क्या होगा?

If \(k_1=80\) and \(k_n=\frac{k_{n-1}}{2}+n\), what is the value of \(k_5\)?

Explanation opens after your attempt
Correct Answer

D. तेरह(13)

Explanation

Simple Explanation

\(k_2=42\), \(k_3=24\), \(k_4=16\) और \(k_5=13\) है। परीक्षा में आधा करने के बाद (n) जोड़ें। / \(k_2=42\), \(k_3=24\), \(k_4=16\), and \(k_5=13\). In exams, add (n) after halving the previous term.

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Question 112/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(m_1=2\) और \(m_n=3m_{n-1}+n-2\) है। \(m_4\) का मान क्या होगा?

In a sequence, \(m_1=2\) and \(m_n=3m_{n-1}+n-2\). What is the value of \(m_4\)?

Explanation opens after your attempt
Correct Answer

A. उनसठ(59)

Explanation

Simple Explanation

\(m_2=6\), \(m_3=19\) और \(m_4=59\) मिलता है। परीक्षा में (n-2) को अलग से जोड़ें। / \(m_2=6\), \(m_3=19\), and \(m_4=59\). In exams, add (n-2) separately.

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Question 113/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(N_1=8\) और (N_n=2N_{n-1}-n(n-1)) है, तो \(N_4\) का मान क्या होगा?

If \(N_1=8\) and (N_n=2N_{n-1}-n(n-1)), what is the value of \(N_4\)?

Explanation opens after your attempt
Correct Answer

C. बत्तीस(32)

Explanation

Simple Explanation

\(N_2=14\), \(N_3=22\) और \(N_4=32\) है। परीक्षा में (n(n-1)) को घटाना है। / \(N_2=14\), \(N_3=22\), and \(N_4=32\). In exams, (n(n-1)) must be subtracted.

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Question 114/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(r_1=4\), \(r_2=6\) और \(r_n=2r_{n-1}-r_{n-2}+n\) है, तो \(r_5\) का मान क्या होगा?

If \(r_1=4\), \(r_2=6\), and \(r_n=2r_{n-1}-r_{n-2}+n\), what is the value of \(r_5\)?

Explanation opens after your attempt
Correct Answer

B. चौंतीस(34)

Explanation

Simple Explanation

\(r_3=11\), \(r_4=20\) और \(r_5=34\) मिलता है। परीक्षा में घटाए जाने वाले पुराने पद का क्रम न बदलें। / \(r_3=11\), \(r_4=20\), and \(r_5=34\). In exams, do not change the order of the older term being subtracted.

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Question 115/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(s_1=5\) और (s_n=s_{n-1}+(-1)^{n+1}(2n-1)) है। \(s_5\) का मान क्या होगा?

In a sequence, \(s_1=5\) and (s_n=s_{n-1}+(-1)^{n+1}(2n-1)). What is the value of \(s_5\)?

Explanation opens after your attempt
Correct Answer

D. नौ(9)

Explanation

Simple Explanation

\(s_2=2\), \(s_3=7\), \(s_4=0\) और \(s_5=9\) है। परीक्षा में विषम जोड़ और घटाव के चिह्न अलग रखें। / \(s_2=2\), \(s_3=7\), \(s_4=0\), and \(s_5=9\). In exams, keep the signs of odd additions and subtractions separate.

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Question 116/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(t_1=x\), \(t_n=2t_{n-1}+3\) और \(t_4=61\) है, तो (x) का मान क्या होगा?

If \(t_1=x\), \(t_n=2t_{n-1}+3\), and \(t_4=61\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

A. पाँच(5)

Explanation

Simple Explanation

\(t_4=8x+21\), इसलिए (x=5) है। परीक्षा में नियम को \(t_1\) तक फैलाकर हल करें। / \(t_4=8x+21\), so (x=5). In exams, expand the rule up to \(t_1\) and solve.

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Question 117/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

अनुक्रम (7), (17), (37), (77) के लिए सही पुनरावर्ती नियम कौन-सा है?

Which recursive rule is correct for the sequence (7), (17), (37), (77)?

Explanation opens after your attempt
Correct Answer

C. नियम \(v_n=2v_{n-1}+3\)Rule \(v_n=2v_{n-1}+3\)

Explanation

Simple Explanation

हर नया पद पिछले पद के दोगुने में (3) जोड़ने से मिलता है। परीक्षा में केवल अंतर नहीं, नियम भी जाँचें। / Each new term is obtained by doubling the previous term and adding (3). In exams, check the rule, not only the difference.

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Question 118/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(v_1=3\) और \(v_n=v_{n-1}+n^3\) है, तो \(v_4\) का मान क्या होगा?

If \(v_1=3\) and \(v_n=v_{n-1}+n^3\), what is the value of \(v_4\)?

Explanation opens after your attempt
Correct Answer

B. एक सौ दो(102)

Explanation

Simple Explanation

\(v_4=3+8+27+64=102\) है। परीक्षा में घन \(n^3\) को सही जोड़ें। / \(v_4=3+8+27+64=102\). In exams, add the cube \(n^3\) correctly.

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Question 119/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(w_1=1\) और \(w_n=w_{n-1}+3^{n-1}+1\) है। \(w_4\) का मान क्या होगा?

In a sequence, \(w_1=1\) and \(w_n=w_{n-1}+3^{n-1}+1\). What is the value of \(w_4\)?

Explanation opens after your attempt
Correct Answer

D. तैंतालीस(43)

Explanation

Simple Explanation

\(w_2=5\), \(w_3=15\) और \(w_4=43\) है। परीक्षा में \(3^{n-1}\) के बाद (1) भी जोड़ें। / \(w_2=5\), \(w_3=15\), and \(w_4=43\). In exams, add (1) after \(3^{n-1}\) too.

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Question 120/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(x_1=4\) और \(x_n=2x_{n-1}+n^2-n\) है, तो \(x_4\) का मान क्या होगा?

If \(x_1=4\) and \(x_n=2x_{n-1}+n^2-n\), what is the value of \(x_4\)?

Explanation opens after your attempt
Correct Answer

A. चौंसठ(64)

Explanation

Simple Explanation

\(x_2=10\), \(x_3=26\) और \(x_4=64\) है। परीक्षा में \(n^2-n\) को सरल करके जोड़ें। / \(x_2=10\), \(x_3=26\), and \(x_4=64\). In exams, simplify \(n^2-n\) before adding it.

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Question 121/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(y_1=2\) और (y_n=y_{n-1}+(2n-1)2) है। \(y_4\) का मान क्या होगा?

In a sequence, \(y_1=2\) and (y_n=y_{n-1}+(2n-1)2). What is the value of \(y_4\)?

Explanation opens after your attempt
Correct Answer

C. पचासी(85)

Explanation

Simple Explanation

\(y_4=2+9+25+49=85\) है। परीक्षा में (2n-1) का वर्ग लेना न भूलें। / \(y_4=2+9+25+49=85\). In exams, remember to square (2n-1).

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Question 122/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(z_1=1\), \(z_2=3\) और \(z_n=z_{n-1}z_{n-2}+n\) है, तो \(z_5\) का मान क्या होगा?

If \(z_1=1\), \(z_2=3\), and \(z_n=z_{n-1}z_{n-2}+n\), what is the value of \(z_5\)?

Explanation opens after your attempt
Correct Answer

B. एक सौ सैंतीस(137)

Explanation

Simple Explanation

\(z_3=6\), \(z_4=22\) और \(z_5=137\) है। परीक्षा में पिछले दो पदों का गुणन करके (n) जोड़ें। / \(z_3=6\), \(z_4=22\), and \(z_5=137\). In exams, multiply the previous two terms and then add (n).

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Question 123/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(A_1=2\) और (A_n=(n+1)A_{n-1}+2) है। \(A_3\) का मान क्या होगा?

In a sequence, \(A_1=2\) and (A_n=(n+1)A_{n-1}+2). What is the value of \(A_3\)?

Explanation opens after your attempt
Correct Answer

D. चौंतीस(34)

Explanation

Simple Explanation

\(A_2=8\) और \(A_3=34\) है। परीक्षा में गुणक (n+1) को सही लगाएँ। / \(A_2=8\) and \(A_3=34\). In exams, apply the multiplier (n+1) correctly.

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Question 124/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(B_1=11\) और \(B_n=B_{n-1}+2^n-n\) है, तो \(B_4\) का मान क्या होगा?

If \(B_1=11\) and \(B_n=B_{n-1}+2^n-n\), what is the value of \(B_4\)?

Explanation opens after your attempt
Correct Answer

A. तीस(30)

Explanation

Simple Explanation

\(B_4=11+2+5+12=30\) है। परीक्षा में \(2^n-n\) को हर चरण पर निकालें। / \(B_4=11+2+5+12=30\). In exams, calculate \(2^n-n\) at each step.

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Question 125/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(C_1=4\) और (C_n=C_{n-1}+n(n+2)) है। \(C_4\) का मान क्या होगा?

In a sequence, \(C_1=4\) and (C_n=C_{n-1}+n(n+2)). What is the value of \(C_4\)?

Explanation opens after your attempt
Correct Answer

C. इक्यावन(51)

Explanation

Simple Explanation

\(C_4=4+8+15+24=51\) है। परीक्षा में (n(n+2)) को पहले सरल करें। / \(C_4=4+8+15+24=51\). In exams, simplify (n(n+2)) first.

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Question 126/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(D_1=5\) और (D_n=3D_{n-1}-(n+1)) है, तो \(D_4\) का मान क्या होगा?

If \(D_1=5\) and (D_n=3D_{n-1}-(n+1)), what is the value of \(D_4\)?

Explanation opens after your attempt
Correct Answer

B. इक्यानवे(91)

Explanation

Simple Explanation

\(D_2=12\), \(D_3=32\) और \(D_4=91\) मिलता है। परीक्षा में (n+1) को घटाना न भूलें। / \(D_2=12\), \(D_3=32\), and \(D_4=91\). In exams, do not forget to subtract (n+1).

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Question 127/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(E_1=2\), \(E_2=4\) और \(E_n=E_{n-1}+E_{n-2}+n\) है, तो \(E_5\) का मान क्या होगा?

If \(E_1=2\), \(E_2=4\), and \(E_n=E_{n-1}+E_{n-2}+n\), what is the value of \(E_5\)?

Explanation opens after your attempt
Correct Answer

D. इकतीस(31)

Explanation

Simple Explanation

\(E_3=9\), \(E_4=17\) और \(E_5=31\) है। परीक्षा में दोनों पिछले पदों के साथ (n) जोड़ें। / \(E_3=9\), \(E_4=17\), and \(E_5=31\). In exams, add (n) along with both previous terms.

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Question 128/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(F_1=90\) और (F_n=F_{n-1}-n(n+1)) है। \(F_4\) का मान क्या होगा?

In a sequence, \(F_1=90\) and (F_n=F_{n-1}-n(n+1)). What is the value of \(F_4\)?

Explanation opens after your attempt
Correct Answer

A. बावन(52)

Explanation

Simple Explanation

\(F_4=90-6-12-20=52\) है। परीक्षा में (n(n+1)) को घटाएँ, जोड़ें नहीं। / \(F_4=90-6-12-20=52\). In exams, subtract (n(n+1)), do not add it.

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Question 129/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(G_1=1\) और \(G_n=2G_{n-1}+2n+1\) है, तो \(G_4\) का मान क्या होगा?

If \(G_1=1\) and \(G_n=2G_{n-1}+2n+1\), what is the value of \(G_4\)?

Explanation opens after your attempt
Correct Answer

C. इक्यावन(51)

Explanation

Simple Explanation

\(G_2=7\), \(G_3=21\) और \(G_4=51\) है। परीक्षा में दोगुना करने के बाद (2n+1) जोड़ें। / \(G_2=7\), \(G_3=21\), and \(G_4=51\). In exams, add (2n+1) after doubling.

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Question 130/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(H_1=6\) और (H_n=H_{n-1}+(n-1)(n+1)) है। \(H_5\) का मान क्या होगा?

In a sequence, \(H_1=6\) and (H_n=H_{n-1}+(n-1)(n+1)). What is the value of \(H_5\)?

Explanation opens after your attempt
Correct Answer

B. छप्पन(56)

Explanation

Simple Explanation

\(H_5=6+3+8+15+24=56\) है। परीक्षा में ((n-1)(n+1)) को सही सरल करें। / \(H_5=6+3+8+15+24=56\). In exams, simplify ((n-1)(n+1)) correctly.

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Question 131/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(J_1=40\) और (J_n=J_{n-1}-4(n-1)+1) है, तो \(J_5\) का मान क्या होगा?

If \(J_1=40\) and (J_n=J_{n-1}-4(n-1)+1), what is the value of \(J_5\)?

Explanation opens after your attempt
Correct Answer

D. चार(4)

Explanation

Simple Explanation

\(J_2=37\), \(J_3=30\), \(J_4=19\) और \(J_5=4\) है। परीक्षा में घटाव और अंत में (1) जोड़ना दोनों करें। / \(J_2=37\), \(J_3=30\), \(J_4=19\), and \(J_5=4\). In exams, handle both the subtraction and final addition of (1).

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Question 132/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(K_1=2\), \(K_2=5\) और \(K_n=3K_{n-1}-K_{n-2}\) है, तो \(K_5\) का मान क्या होगा?

If \(K_1=2\), \(K_2=5\), and \(K_n=3K_{n-1}-K_{n-2}\), what is the value of \(K_5\)?

Explanation opens after your attempt
Correct Answer

A. नवासी(89)

Explanation

Simple Explanation

\(K_3=13\), \(K_4=34\) और \(K_5=89\) है। परीक्षा में पिछले पद का (3) गुना लेकर उससे पहले वाला पद घटाएँ। / \(K_3=13\), \(K_4=34\), and \(K_5=89\). In exams, triple the previous term and subtract the term before it.

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Question 133/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(L_1=4\) और \(L_n=L_{n-1}+5n-4\) है। \(L_5\) का मान क्या होगा?

In a sequence, \(L_1=4\) and \(L_n=L_{n-1}+5n-4\). What is the value of \(L_5\)?

Explanation opens after your attempt
Correct Answer

C. अट्ठावन(58)

Explanation

Simple Explanation

\(L_5=4+6+11+16+21=58\) है। परीक्षा में (5n-4) से बनने वाली राशियाँ क्रम से जोड़ें। / \(L_5=4+6+11+16+21=58\). In exams, add the quantities formed by (5n-4) in order.

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Question 134/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(M_1=2\) और \(M_n=4M_{n-1}-n\) है, तो \(M_3\) का मान क्या होगा?

If \(M_1=2\) and \(M_n=4M_{n-1}-n\), what is the value of \(M_3\)?

Explanation opens after your attempt
Correct Answer

B. इक्कीस(21)

Explanation

Simple Explanation

\(M_2=6\) और \(M_3=21\) है। परीक्षा में (4) से गुणा करके वर्तमान (n) घटाएँ। / \(M_2=6\) and \(M_3=21\). In exams, multiply by (4) and subtract the current (n).

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Question 135/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(R_1=1\) और (R_n=(n+2)R_{n-1}-1) है। \(R_4\) का मान क्या होगा?

In a sequence, \(R_1=1\) and (R_n=(n+2)R_{n-1}-1). What is the value of \(R_4\)?

Explanation opens after your attempt
Correct Answer

D. तिरासी(83)

Explanation

Simple Explanation

\(R_2=3\), \(R_3=14\) और \(R_4=83\) मिलता है। परीक्षा में गुणक (n+2) को हर चरण पर बदलें। / \(R_2=3\), \(R_3=14\), and \(R_4=83\). In exams, change the multiplier (n+2) at every step.

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Question 136/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(O_1=5\) और \(O_n=O_{n-1}+2^n+2n\) है, तो \(O_4\) का मान क्या होगा?

If \(O_1=5\) and \(O_n=O_{n-1}+2^n+2n\), what is the value of \(O_4\)?

Explanation opens after your attempt
Correct Answer

A. इक्यावन(51)

Explanation

Simple Explanation

\(O_2=13\), \(O_3=27\) और \(O_4=51\) है। परीक्षा में घात और (2n) दोनों जोड़ें। / \(O_2=13\), \(O_3=27\), and \(O_4=51\). In exams, add both the power and (2n).

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Question 137/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(P_1=0\) और \(P_n=P_{n-1}+3n^2-1\) है। \(P_4\) का मान क्या होगा?

In a sequence, \(P_1=0\) and \(P_n=P_{n-1}+3n^2-1\). What is the value of \(P_4\)?

Explanation opens after your attempt
Correct Answer

C. चौरासी(84)

Explanation

Simple Explanation

\(P_4=0+11+26+47=84\) है। परीक्षा में \(3n^2-1\) को पहले निकालें। / \(P_4=0+11+26+47=84\). In exams, calculate \(3n^2-1\) first.

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Question 138/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(Q_1=1\), \(Q_2=2\) और \(Q_n=Q_{n-1}+Q_{n-2}+n^2\) है, तो \(Q_5\) का मान क्या होगा?

If \(Q_1=1\), \(Q_2=2\), and \(Q_n=Q_{n-1}+Q_{n-2}+n^2\), what is the value of \(Q_5\)?

Explanation opens after your attempt
Correct Answer

B. सड़सठ(67)

Explanation

Simple Explanation

\(Q_3=12\), \(Q_4=30\) और \(Q_5=67\) है। परीक्षा में दोनों पिछले पदों के साथ \(n^2\) जोड़ें। / \(Q_3=12\), \(Q_4=30\), and \(Q_5=67\). In exams, add \(n^2\) with both previous terms.

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Question 139/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(U_1=3\) और \(U_n=U_{n-1}^2-n\) है, तो \(U_3\) का मान क्या होगा?

If \(U_1=3\) and \(U_n=U_{n-1}^2-n\), what is the value of \(U_3\)?

Explanation opens after your attempt
Correct Answer

D. छियालीस(46)

Explanation

Simple Explanation

\(U_2=7\) और \(U_3=46\) है। परीक्षा में पिछले पद का वर्ग लेकर वर्तमान (n) घटाएँ। / \(U_2=7\) and \(U_3=46\). In exams, square the previous term and subtract the current (n).

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Question 140/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम में \(S_1=75\) और \(S_n=S_{n-1}-2^n\) है। \(S_4\) का मान क्या होगा?

In a sequence, \(S_1=75\) and \(S_n=S_{n-1}-2^n\). What is the value of \(S_4\)?

Explanation opens after your attempt
Correct Answer

A. सैंतालीस(47)

Explanation

Simple Explanation

\(S_4=75-4-8-16=47\) है। परीक्षा में \(2^n\) को घटाना है। / \(S_4=75-4-8-16=47\). In exams, \(2^n\) must be subtracted.

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Question 141/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(T_1=2\) और (T_n=(n+2)T_{n-1}+n) है, तो \(T_3\) का मान क्या होगा?

If \(T_1=2\) and (T_n=(n+2)T_{n-1}+n), what is the value of \(T_3\)?

Explanation opens after your attempt
Correct Answer

C. तिरेपन(53)

Explanation

Simple Explanation

\(T_2=10\) और \(T_3=53\) है। परीक्षा में (n+2) से गुणा करके (n) जोड़ें। / \(T_2=10\) and \(T_3=53\). In exams, multiply by (n+2) and add (n).

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Question 142/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

किसी अनुक्रम के पहले चार पद (4), (10), (22), (46) हैं और नियम \(a_n=2a_{n-1}+2\) है। \(a_5\) क्या होगा?

The first four terms of a sequence are (4), (10), (22), (46), and the rule is \(a_n=2a_{n-1}+2\). What is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. चौरानवे(94)

Explanation

Simple Explanation

\(a_5=2\times 46+2=94\) है। परीक्षा में अंतिम दिए पद पर नियम लगाएँ। / \(a_5=2\times 46+2=94\). In exams, apply the rule to the last given term.

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Question 143/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(a_n=a_{n-1}+4n-2\) और \(a_5=70\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=a_{n-1}+4n-2\) and \(a_5=70\), what is the value of \(a_2\)?

Explanation opens after your attempt
Correct Answer

D. अट्ठाईस(28)

Explanation

Simple Explanation

\(a_5=a_2+10+14+18\), इसलिए \(a_2=28\) है। परीक्षा में बीच के पद के लिए आगे की जोड़ घटाएँ। / \(a_5=a_2+10+14+18\), so \(a_2=28\). In exams, subtract the later additions to find a middle term.

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Question 144/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(b_n=3b_{n-1}+2\) और \(b_3=44\) है, तो \(b_1\) का मान क्या होगा?

If \(b_n=3b_{n-1}+2\) and \(b_3=44\), what is the value of \(b_1\)?

Explanation opens after your attempt
Correct Answer

A. चार(4)

Explanation

Simple Explanation

\(b_3=9b_1+8\), इसलिए \(b_1=4\) है। परीक्षा में पुनरावर्ती नियम को पहले पद तक फैलाएँ। / \(b_3=9b_1+8\), so \(b_1=4\). In exams, expand the recursive rule up to the first term.

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Question 145/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(c_1=3\) और (c_n=c_{n-1}+n(n-1)) है, तो कौन-सा कथन सही है?

If \(c_1=3\) and (c_n=c_{n-1}+n(n-1)), which statement is correct?

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Correct Answer

C. \(c_2=5\) और \(c_3=11\)\(c_2=5\) and \(c_3=11\)

Explanation

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\(c_2=3+2=5\) और \(c_3=5+6=11\) है। परीक्षा में (n(n-1)) को हर पद पर नया निकालें। / \(c_2=3+2=5\) and \(c_3=5+6=11\). In exams, calculate (n(n-1)) newly for each term.

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Question 146/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(d_1=2\) और \(d_n=d_{n-1}+4n\) है, तो \(d_n>60\) पहली बार किस (n) पर होगा?

If \(d_1=2\) and \(d_n=d_{n-1}+4n\), for which (n) will \(d_n>60\) first occur?

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Correct Answer

D. छह(6)

Explanation

Simple Explanation

\(d_5=58\) और \(d_6=82\), इसलिए पहली बार (n=6) पर मान (60) से अधिक होता है। परीक्षा में पहले से अधिक होने वाला पद चुनें। / \(d_5=58\) and \(d_6=82\), so the value first exceeds (60) at (n=6). In exams, choose the first term that becomes greater.

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Question 147/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(e_1=2\) और \(e_n=3e_{n-1}-n\) है, तो \(e_4-e_3\) का मान क्या होगा?

If \(e_1=2\) and \(e_n=3e_{n-1}-n\), what is the value of \(e_4-e_3\)?

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Correct Answer

B. चौदह(14)

Explanation

Simple Explanation

\(e_3=9\) और \(e_4=23\), इसलिए अंतर (14) है। परीक्षा में अंतर निकालने से पहले दोनों पद सही निकालें। / \(e_3=9\) and \(e_4=23\), so the difference is (14). In exams, find both terms correctly before taking the difference.

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Question 148/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(f_1=3\) और \(f_n=f_{n-1}+3n-1\) है, तो पहले चार पदों का योग क्या होगा?

If \(f_1=3\) and \(f_n=f_{n-1}+3n-1\), what is the sum of the first four terms?

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Correct Answer

A. चौवन(54)

Explanation

Simple Explanation

पहले चार पद (3), (8), (16), (27) हैं और उनका योग (54) है। परीक्षा में योग के लिए सभी आवश्यक पद जोड़ें। / The first four terms are (3), (8), (16), and (27), and their sum is (54). In exams, add all required terms for a sum.

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Question 149/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(g_1=2\) और \(g_n=2g_{n-1}+1\) है, तो \(g_5:g_4\) क्या होगा?

If \(g_1=2\) and \(g_n=2g_{n-1}+1\), what is \(g_5:g_4\)?

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Correct Answer

D. (47:23)

Explanation

Simple Explanation

\(g_4=23\) और \(g_5=47\), इसलिए अनुपात (47:23) है। परीक्षा में अनुपात का क्रम न बदलें। / \(g_4=23\) and \(g_5=47\), so the ratio is (47:23). In exams, do not reverse the order of the ratio.

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Question 150/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(h_1=3\), \(h_2=8\) और \(h_n=2h_{n-1}-h_{n-2}+2n\) है, तो \(h_5\) का मान क्या होगा?

If \(h_1=3\), \(h_2=8\), and \(h_n=2h_{n-1}-h_{n-2}+2n\), what is the value of \(h_5\)?

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Correct Answer

C. सड़सठ(67)

Explanation

Simple Explanation

\(h_3=19\), \(h_4=38\) और \(h_5=67\) है। परीक्षा में घटाव वाले पुराने पद को सही रखें। / \(h_3=19\), \(h_4=38\), and \(h_5=67\). In exams, keep the older subtracted term correct.

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Question 151/151 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 46

यदि \(p_1=2\) और \(p_n=p_{n-1}+n^2+n+1\) है, तो \(p_5\) का मान क्या होगा?

If \(p_1=2\) and \(p_n=p_{n-1}+n^2+n+1\), what is the value of \(p_5\)?

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Correct Answer

B. चौहत्तर(74)

Explanation

Simple Explanation

\(p_5=2+7+13+21+31=74\) है। परीक्षा में \(n^2+n+1\) को पहले सरल करके जोड़ें। / \(p_5=2+7+13+21+31=74\). In exams, simplify \(n^2+n+1\) first and then add.

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