Class 9 Mathematics - Sequences and Progressions - Sum of first n natural numbers Hard Quiz

Mathematics Sequences and Progressions Sum of first n natural numbers Hard Class 9 Level 43

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Question 1/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(16,25,36,49,64,\ldots\) का (8)वाँ पद क्या होगा?

What will be the (8)th term of \(16,25,36,49,64,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (121)

Explanation

Simple Explanation

यह \(4^2,5^2,6^2,\ldots\) का क्रम है। (8)वाँ पद \(11^2=121\) होगा। / This is the sequence \(4^2,5^2,6^2,\ldots\). The (8)th term will be \(11^2=121\).

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Question 2/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(64,125,216,343,\ldots\) का (6)ठा पद क्या है?

What is the (6)th term of \(64,125,216,343,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (729)

Explanation

Simple Explanation

यह \(4^3,5^3,6^3,7^3,\ldots\) का क्रम है। (6)ठा पद \(9^3=729\) है। / This is the sequence \(4^3,5^3,6^3,7^3,\ldots\). The (6)th term is \(9^3=729\).

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Question 3/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(4,10,14,24,38,\ldots\) का अगला पद क्या है यदि हर नया पद पिछले दो पदों का योग है?

What is the next term of \(4,10,14,24,38,\ldots\) if each new term is the sum of the previous two terms?

Explanation opens after your attempt

Correct Answer

C. (62)

Explanation

Simple Explanation

यहाँ (14=4+10), (24=10+14) और (38=14+24) है। अगला पद (24+38=62) होगा। / Here (14=4+10), (24=10+14), and (38=14+24). The next term will be (24+38=62).

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Question 4/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि किसी क्रम के पहले चार पद (9,20,31,42) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?

If the first four terms of a sequence are (9,20,31,42), what can be a simple rule for \(a_n\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=11n-2\)

Explanation

Simple Explanation

पहला पद (9) और अंतर (11) है। \(a_n=11n-2\) से वही क्रम मिलता है। / The first term is (9) and the difference is (11). \(a_n=11n-2\) gives the same sequence.

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Question 5/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

नियम \(a_n=8n-5\) से बनने वाले पहले चार पद कौन से हैं?

What are the first four terms formed by \(a_n=8n-5\)?

Explanation opens after your attempt

Correct Answer

A. (3,11,19,27)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (3,11,19,27) मिलते हैं। पहले पद के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (3,11,19,27). Start with (n=1) for the first term.

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Question 6/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

कौन सा क्रम \(a_n=3^n+n\) से बने पहले चार पद दिखाता है?

Which sequence shows the first four terms of \(a_n=3^n+n\)?

Explanation opens after your attempt

Correct Answer

A. (4,11,30,85)

Explanation

Simple Explanation

\(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), \(3^4+4=85\)। घात के बाद (n) जोड़ें। / \(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), and \(3^4+4=85\). Add (n) after evaluating the power.

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Question 7/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(8,16,24,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of \(8,16,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (360)

Explanation

Simple Explanation

पहले (9) पद (8) से (72) तक हैं। उनका योग (360) है। / The first (9) terms run from (8) to (72). Their sum is (360).

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Question 8/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(132,121,110,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of \(132,121,110,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (627)

Explanation

Simple Explanation

पहले (6) पद (132,121,110,99,88,77) हैं। इनका योग (627) है। / The first (6) terms are (132,121,110,99,88,77). Their sum is (627).

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Question 9/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(11,17,23,29,\ldots\) में \(a_8+a_9\) का मान क्या है?

What is the value of \(a_8+a_9\) in \(11,17,23,29,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (106)

Explanation

Simple Explanation

\(a_8=53\) और \(a_9=59\) है। इसलिए \(a_8+a_9=112\), अतः विकल्पों में सही मान नहीं है। / \(a_8=53\) and \(a_9=59\). Therefore \(a_8+a_9=112\), so the correct value is not in the options.

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Question 10/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(12,21,30,39,\ldots\) में पहले कितने पदों का योग (150) है?

How many first terms of \(12,21,30,39,\ldots\) have sum (150)?

Explanation opens after your attempt

Correct Answer

B. (5)

Explanation

Simple Explanation

पहले (5) पद (12,21,30,39,48) हैं। उनका योग (150) है। / The first (5) terms are (12,21,30,39,48). Their sum is (150).

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Question 11/11 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=9\), \(a_2=16\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_6\) क्या होगा?

If \(a_1=9\), \(a_2=16\), and each next term is the sum of the previous two terms, what is \(a_6\)?

Explanation opens after your attempt

Correct Answer

D. (107)

Explanation

Simple Explanation

क्रम (9,16,25,41,66,107) बनेगा। इसलिए \(a_6=107\) है। / The sequence becomes (9,16,25,41,66,107). Therefore \(a_6=107\).

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Class 9 Mathematics - Sequences and Progressions - Sum of first n natural numbers Hard Quiz

क्रम \(16,25,36,49,64,\ldots\) का (8)वाँ पद क्या होगा?

Simple Explanation

क्रम \(64,125,216,343,\ldots\) का (6)ठा पद क्या है?

Simple Explanation

क्रम \(4,10,14,24,38,\ldots\) का अगला पद क्या है यदि हर नया पद पिछले दो पदों का योग है?

Simple Explanation

यदि किसी क्रम के पहले चार पद (9,20,31,42) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?

Simple Explanation

नियम \(a_n=8n-5\) से बनने वाले पहले चार पद कौन से हैं?

Simple Explanation

कौन सा क्रम \(a_n=3^n+n\) से बने पहले चार पद दिखाता है?

Simple Explanation

क्रम \(8,16,24,\ldots\) के पहले (9) पदों का योग क्या है?

Simple Explanation

क्रम \(132,121,110,\ldots\) के पहले (6) पदों का योग क्या है?

Simple Explanation

क्रम \(11,17,23,29,\ldots\) में \(a_8+a_9\) का मान क्या है?

Simple Explanation

क्रम \(12,21,30,39,\ldots\) में पहले कितने पदों का योग (150) है?

Simple Explanation

यदि \(a_1=9\), \(a_2=16\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_6\) क्या होगा?

Simple Explanation

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