Class 9 Mathematics - Sequences and Progressions - nth term Hard Quiz

Mathematics Sequences and Progressions nth term Hard Class 9 Level 47

Level 47 • 16/50 questions • 30 seconds per question.

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This level needs 34 more active questions. Admin panel me same class, subject, difficulty aur level_no 47 par question add karein.
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Question 1/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

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

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

Explanation opens after your attempt
Correct Answer

B. (90)

Step 1

Concept

The terms are (2,7,16,39,94), so \(a_5=94\). Exam tip: use both previous terms carefully.

Step 2

Why this answer is correct

The correct answer is B. (90). The terms are (2,7,16,39,94), so \(a_5=94\). Exam tip: use both previous terms carefully.

Step 3

Exam Tip

पद (2,7,16,39,94) हैं इसलिए \(a_5=94\) है। सही विकल्पों में (94) होना चाहिए।

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Question 2/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

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

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

Explanation opens after your attempt
Correct Answer

C. (39)

Step 1

Concept

\(a_3=2\times7+2=16\) and \(a_4=2\times16+7=39\). Exam tip: write positions while using a two-term rule.

Step 2

Why this answer is correct

The correct answer is C. (39). \(a_3=2\times7+2=16\) and \(a_4=2\times16+7=39\). Exam tip: write positions while using a two-term rule.

Step 3

Exam Tip

\(a_3=2\times7+2=16\) और \(a_4=2\times16+7=39\) है। दो-पद नियम में क्रमांक साथ लिखें।

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Question 3/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=10\) और \(a_{n+1}=a_n+2a_1+n^2\) है तो \(a_3\) क्या होगा?

If \(a_1=10\) and \(a_{n+1}=a_n+2a_1+n^2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

B. (54)

Step 1

Concept

\(a_2=10+20+1=31\) and \(a_3=31+20+4=55\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 2

Why this answer is correct

The correct answer is B. (54). \(a_2=10+20+1=31\) and \(a_3=31+20+4=55\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 3

Exam Tip

\(a_2=10+20+1=31\) और \(a_3=31+20+4=55\) है। सही विकल्पों में (55) होना चाहिए।

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Question 4/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=2\), \(a_2=6\) और \(a_n=a_{n-1}+a_{n-2}+3n\) है तो \(a_5\) क्या होगा?

If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+3n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

B. (50)

Step 1

Concept

\(a_3=17\), \(a_4=35\), and \(a_5=67\). Exam tip: add current (3n) with the previous two terms.

Step 2

Why this answer is correct

The correct answer is B. (50). \(a_3=17\), \(a_4=35\), and \(a_5=67\). Exam tip: add current (3n) with the previous two terms.

Step 3

Exam Tip

\(a_3=17\), \(a_4=35\) और \(a_5=67\) है। सही विकल्पों में (67) होना चाहिए।

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Question 5/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

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

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

Explanation opens after your attempt
Correct Answer

D. (35)

Step 1

Concept

\(a_3=6+2+9=17\) and \(a_4=17+6+12=35\). Exam tip: use the correct current value of (n).

Step 2

Why this answer is correct

The correct answer is D. (35). \(a_3=6+2+9=17\) and \(a_4=17+6+12=35\). Exam tip: use the correct current value of (n).

Step 3

Exam Tip

\(a_3=6+2+9=17\) और \(a_4=17+6+12=35\) है। वर्तमान (n) का सही मान रखें।

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Question 6/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=11\) और \(a_{n+1}=a_n+7\) है तो कौन सा पद (74) है?

If \(a_1=11\) and \(a_{n+1}=a_n+7\), which term is (74)?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Step 1

Concept

(74-11=63), and \(63\div7=9\) steps, so the term number is (10). Exam tip: add (1) to the number of steps.

Step 2

Why this answer is correct

The correct answer is C. (10)वाँ / (10)th. (74-11=63), and \(63\div7=9\) steps, so the term number is (10). Exam tip: add (1) to the number of steps.

Step 3

Exam Tip

(74-11=63) और \(63\div7=9\) चरण हैं इसलिए पद संख्या (10) है। चरणों में (1) जोड़कर पद संख्या मिलती है।

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Question 7/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

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

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

Explanation opens after your attempt
Correct Answer

C. (70)

Step 1

Concept

The terms are (4,15,37,81), so \(a_4-a_2=66\). Exam tip: find both terms first and subtract.

Step 2

Why this answer is correct

The correct answer is C. (70). The terms are (4,15,37,81), so \(a_4-a_2=66\). Exam tip: find both terms first and subtract.

Step 3

Exam Tip

पद (4,15,37,81) हैं इसलिए \(a_4-a_2=66\) है। सही विकल्पों में (66) होना चाहिए।

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Question 8/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=4\) और \(a_{n+1}=2a_n+7\) है तो \(a_3-a_2\) का मान क्या होगा?

If \(a_1=4\) and \(a_{n+1}=2a_n+7\), what is the value of \(a_3-a_2\)?

Explanation opens after your attempt
Correct Answer

C. (22)

Step 1

Concept

The terms are (4,15,37), so \(a_3-a_2=22\). Exam tip: find both terms before taking the difference.

Step 2

Why this answer is correct

The correct answer is C. (22). The terms are (4,15,37), so \(a_3-a_2=22\). Exam tip: find both terms before taking the difference.

Step 3

Exam Tip

पद (4,15,37) हैं इसलिए \(a_3-a_2=22\) है। पहले दोनों पद निकालें फिर अंतर लें।

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Question 9/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=4\), \(a_2=8\) और \(a_n=a_{n-1}+a_{n-2}+6\) है तो \(a_5\) क्या होगा?

If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (54)

Step 1

Concept

The terms are (4,8,18,32,56), so \(a_5=56\). Exam tip: add (6) along with the previous two terms.

Step 2

Why this answer is correct

The correct answer is A. (54). The terms are (4,8,18,32,56), so \(a_5=56\). Exam tip: add (6) along with the previous two terms.

Step 3

Exam Tip

पद (4,8,18,32,56) हैं इसलिए \(a_5=56\) है। सही विकल्पों में (56) होना चाहिए।

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Question 10/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=4\), \(a_2=8\) और \(a_n=a_{n-1}+a_{n-2}+6\) है तो \(a_4\) क्या होगा?

If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

D. (32)

Step 1

Concept

\(a_3=8+4+6=18\) and \(a_4=18+8+6=32\). Exam tip: add the extra constant at every step.

Step 2

Why this answer is correct

The correct answer is D. (32). \(a_3=8+4+6=18\) and \(a_4=18+8+6=32\). Exam tip: add the extra constant at every step.

Step 3

Exam Tip

\(a_3=8+4+6=18\) और \(a_4=18+8+6=32\) है। अतिरिक्त स्थिरांक हर चरण में जोड़ें।

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Question 11/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=7\) और \(a_{n+1}=a_n+n^2+n\) है तो कौन सा पद (47) है?

If \(a_1=7\) and \(a_{n+1}=a_n+n^2+n\), which term is (47)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (7,9,15,27,47), so (47) is the fifth term. Exam tip: write changing additions to check the position.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (7,9,15,27,47), so (47) is the fifth term. Exam tip: write changing additions to check the position.

Step 3

Exam Tip

पद (7,9,15,27,47) हैं इसलिए (47) पाँचवाँ पद है। बदलते जोड़ लिखकर पद संख्या जाँचें।

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Question 12/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=150\) और (a_{n+1}=a_n-\(n^2+n\)) है तो कौन सा पद (110) है?

If \(a_1=150\) and (a_{n+1}=a_n-\(n^2+n\)), which term is (110)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (150,148,142,130,110), so (110) is the fifth term. Exam tip: write decreasing terms with positions.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (150,148,142,130,110), so (110) is the fifth term. Exam tip: write decreasing terms with positions.

Step 3

Exam Tip

पद (150,148,142,130,110) हैं इसलिए (110) पाँचवाँ पद है। घटते हुए पदों को क्रमांक सहित लिखें।

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Question 13/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=2\), \(a_2=8\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_5\) क्या होगा?

If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (66)

Step 1

Concept

\(a_3=15\), \(a_4=35\), and \(a_5=70\). Exam tip: multiply \(a_{n-2}\) by (2) and add current (n).

Step 2

Why this answer is correct

The correct answer is A. (66). \(a_3=15\), \(a_4=35\), and \(a_5=70\). Exam tip: multiply \(a_{n-2}\) by (2) and add current (n).

Step 3

Exam Tip

\(a_3=15\), \(a_4=35\) और \(a_5=70\) है। सही विकल्पों में (70) होना चाहिए।

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Question 14/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=2\), \(a_2=8\) और \(a_n=a_{n-1}+2a_{n-2}+n\) है तो \(a_4\) क्या होगा?

If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (35)

Step 1

Concept

\(a_3=8+2\times2+3=15\) and \(a_4=15+2\times8+4=35\). Exam tip: do not forget to add current (n).

Step 2

Why this answer is correct

The correct answer is C. (35). \(a_3=8+2\times2+3=15\) and \(a_4=15+2\times8+4=35\). Exam tip: do not forget to add current (n).

Step 3

Exam Tip

\(a_3=8+2\times2+3=15\) और \(a_4=15+2\times8+4=35\) है। वर्तमान (n) भी जोड़ना न भूलें।

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Question 15/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

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

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

Explanation opens after your attempt
Correct Answer

B. (37)

Step 1

Concept

The terms are (6,13,23,38), so \(a_4=38\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 2

Why this answer is correct

The correct answer is B. (37). The terms are (6,13,23,38), so \(a_4=38\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.

Step 3

Exam Tip

पद (6,13,23,38) हैं इसलिए \(a_4=38\) है। सही विकल्पों में (38) होना चाहिए।

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Question 16/16 Hard Mathematics Sequences and Progressions Recursive rule Class 9 Level 47

यदि \(a_1=6\) और \(a_{n+1}=a_n+a_1+n^2\) है तो \(a_3\) क्या होगा?

If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_3\)?

Explanation opens after your attempt
Correct Answer

C. (23)

Step 1

Concept

\(a_2=6+6+1=13\) and \(a_3=13+6+4=23\). Exam tip: \(a_1\) remains fixed.

Step 2

Why this answer is correct

The correct answer is C. (23). \(a_2=6+6+1=13\) and \(a_3=13+6+4=23\). Exam tip: \(a_1\) remains fixed.

Step 3

Exam Tip

\(a_2=6+6+1=13\) और \(a_3=13+6+4=23\) है। \(a_1\) स्थिर रहता है।

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