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Class 9 Mathematics - Exploring Algebraic Identities - Algebraic identities Medium Quiz

Mathematics Exploring Algebraic Identities Algebraic identities Medium Class 9 Level 42

Level 42 • 50/50 questions • 35 seconds per question.

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Question 1/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,10,16,22,\ldots\) का (9)वाँ पद क्या होगा?

What will be the (9)th term of \(4,10,16,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (52)

Explanation

Simple Explanation

पहला पद (4) और समान अंतर (6) है। (9)वाँ पद \(4+8\times6=52\) है। / The first term is (4) and the common difference is (6). The (9)th term is \(4+8\times6=52\).

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Question 2/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(64,58,52,46,\ldots\) का (7)वाँ पद क्या है?

What is the (7)th term of \(64,58,52,46,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (28)

Explanation

Simple Explanation

हर बार (6) घट रहा है। (7)वाँ पद \(64-6\times6=28\) है। / Each term decreases by (6). The (7)th term is \(64-6\times6=28\).

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Question 3/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_n=4n+3\) है, तो \(a_8\) का मान क्या है?

If \(a_n=4n+3\), what is the value of \(a_8\)?

Explanation opens after your attempt
Correct Answer

B. (35)

Explanation

Simple Explanation

(n=8) रखने पर (a_8=4(8)+3=35) है। नियम में (n) का सही मान रखें। / Putting (n=8), (a_8=4(8)+3=35). Substitute the correct value of (n) in the rule.

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Question 4/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_n=3n^2+2\) है, तो \(a_4\) क्या होगा?

If \(a_n=3n^2+2\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (50)

Explanation

Simple Explanation

(n=4) रखने पर (3\(4^2\)+2=50) है। पहले वर्ग निकालें और फिर गुणा करें। / Putting (n=4), (3\(4^2\)+2=50). Square first and then multiply.

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Question 5/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,13,20,\Box,34\) में खाली स्थान का मान क्या है?

What is the missing value in \(6,13,20,\Box,34\)?

Explanation opens after your attempt
Correct Answer

C. (27)

Explanation

Simple Explanation

हर बार (7) जोड़ा जा रहा है। (20+7=27) खाली स्थान है। / Each term increases by (7). (20+7=27) is the missing value.

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Question 6/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(95,\Box,77,68,59\) में खाली स्थान कौन सा है?

Which value fills the blank in \(95,\Box,77,68,59\)?

Explanation opens after your attempt
Correct Answer

B. (86)

Explanation

Simple Explanation

क्रम में हर बार (9) घट रहा है। (95-9=86) होगा। / The sequence decreases by (9) each time. (95-9=86).

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Question 7/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,8,15,24,35,\ldots\) का अगला पद क्या है?

What is the next term of \(3,8,15,24,35,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (48)

Explanation

Simple Explanation

अंतर (5,7,9,11) हैं। अगला अंतर (13) होगा, इसलिए (35+13=48)। / The differences are (5,7,9,11). The next difference is (13), so (35+13=48).

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Question 8/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(120,117,111,102,90,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(120,117,111,102,90,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (75)

Explanation

Simple Explanation

घटाव (3,6,9,12) है और अगला घटाव (15) होगा। (90-15=75) है। / The subtractions are (3,6,9,12), so the next subtraction is (15). (90-15=75).

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

क्रम \(5,15,45,135,\ldots\) का (6)ठा पद क्या है?

What is the (6)th term of \(5,15,45,135,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (1215)

Explanation

Simple Explanation

हर पद पिछले पद का (3) गुना है। (5)वाँ पद (405) और (6)ठा पद (1215) है। / Each term is (3) times the previous term. The (5)th term is (405) and the (6)th term is (1215).

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Question 10/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(512,256,128,64,\ldots\) का अगला पद क्या है?

What is the next term of \(512,256,128,64,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (32)

Explanation

Simple Explanation

हर पद पिछले पद का आधा है। \(64\div2=32\) अगला पद है। / Each term is half of the previous term. \(64\div2=32\) is the next term.

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Question 11/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,9,16,25,36,\ldots\) में (8)वाँ पद क्या होगा?

What will be the (8)th term in \(4,9,16,25,36,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (81)

Explanation

Simple Explanation

यह \(2^2,3^2,4^2,\ldots\) का क्रम है। (8)वाँ पद \(9^2=81\) होगा। / This is the sequence \(2^2,3^2,4^2,\ldots\). The (8)th term will be \(9^2=81\).

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Question 12/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(8,27,64,125,\ldots\) का (5)वाँ पद क्या है?

What is the (5)th term of \(8,27,64,125,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (216)

Explanation

Simple Explanation

यह \(2^3,3^3,4^3,5^3,\ldots\) का क्रम है। (5)वाँ पद \(6^3=216\) है। / This is the sequence \(2^3,3^3,4^3,5^3,\ldots\). The (5)th term is \(6^3=216\).

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Question 13/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(2,5,9,14,20,\ldots\) का (7)वाँ पद क्या है?

What is the (7)th term of \(2,5,9,14,20,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (35)

Explanation

Simple Explanation

अंतर (3,4,5,6) हैं, फिर (7) और (8) जुड़ेंगे। (7)वाँ पद (35) है। / The differences are (3,4,5,6), then (7) and (8) are added. The (7)th term is (35).

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Question 14/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,4,7,11,18,\ldots\) का अगला पद क्या है?

What is the next term of \(3,4,7,11,18,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (29)

Explanation

Simple Explanation

हर पद पिछले दो पदों का योग है। (11+18=29) अगला पद है। / Each term is the sum of the previous two terms. (11+18=29) is the next term.

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Question 15/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(7,12,19,31,50,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(7,12,19,31,50,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (81)

Explanation

Simple Explanation

यहाँ (19=7+12), (31=12+19), (50=19+31) है। अगला पद (31+50=81) होगा। / Here (19=7+12), (31=12+19), and (50=19+31). The next term will be (31+50=81).

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Question 16/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,12,36,108,\ldots\) में (324) कौन सा पद है?

In \(4,12,36,108,\ldots\), which term is (324)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Explanation

Simple Explanation

क्रम (4,12,36,108,324) है। इसलिए (324) (5)वाँ पद है। / The sequence is (4,12,36,108,324). So (324) is the (5)th term.

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Question 17/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(8,15,22,29,\ldots\) में (57) कौन सा पद होगा?

In \(8,15,22,29,\ldots\), which term will (57) be?

Explanation opens after your attempt
Correct Answer

B. (8)वाँ(8)th

Explanation

Simple Explanation

पहला पद (8) और अंतर (7) है। (8+(n-1)7=57) से (n=8) मिलता है। / The first term is (8) and the difference is (7). From (8+(n-1)7=57), (n=8).

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Question 18/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(88,82,76,70,\ldots\) में (52) कौन सा पद है?

In \(88,82,76,70,\ldots\), which term is (52)?

Explanation opens after your attempt
Correct Answer

B. (7)वाँ(7)th

Explanation

Simple Explanation

हर बार (6) घट रहा है। (88-(n-1)6=52) से (n=7) है। / Each term decreases by (6). From (88-(n-1)6=52), (n=7).

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Question 19/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि किसी क्रम के पहले चार पद (3,9,15,21) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?

If the first four terms of a sequence are (3,9,15,21), what can be a simple rule for \(a_n\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=6n-3\)

Explanation

Simple Explanation

पहला पद (3) और अंतर (6) है। \(a_n=6n-3\) से वही क्रम मिलता है। / The first term is (3) and the difference is (6). \(a_n=6n-3\) gives the same sequence.

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Question 20/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,15,24,33,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?

Which \(a_n\) rule is correct for \(6,15,24,33,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=9n-3\)

Explanation

Simple Explanation

पहला पद (6) और अंतर (9) है। \(a_n=9n-3\) से \(6,15,24,\ldots\) मिलते हैं। / The first term is (6) and the difference is (9). \(a_n=9n-3\) gives \(6,15,24,\ldots\).

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Question 21/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=5n+2\) से बनने वाले पहले चार पद कौन से हैं?

What are the first four terms formed by \(a_n=5n+2\)?

Explanation opens after your attempt
Correct Answer

C. (7,12,17,22)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (7,12,17,22) मिलते हैं। पहले चार पदों के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,12,17,22). Start with (n=1) for the first four terms.

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Question 22/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=n^2+3n\) से \(a_5\) क्या होगा?

What will \(a_5\) be for the rule \(a_n=n^2+3n\)?

Explanation opens after your attempt
Correct Answer

B. (40)

Explanation

Simple Explanation

(n=5) रखने पर (a_5=52+3(5)=40) है। वर्ग और गुणा दोनों सावधानी से करें। / Putting (n=5), (a_5=52+3(5)=40). Handle both the square and multiplication carefully.

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Question 23/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=70-5n\) से बनने वाला चौथा पद क्या है?

What is the fourth term formed by \(a_n=70-5n\)?

Explanation opens after your attempt
Correct Answer

B. (50)

Explanation

Simple Explanation

(n=4) रखने पर \(a_4=70-20=50\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें। / Putting (n=4), \(a_4=70-20=50\). Pay attention to the sign in subtraction rules.

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Question 24/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

कौन सा क्रम \(a_n=4n^2\) से बनता है?

Which sequence is formed by \(a_n=4n^2\)?

Explanation opens after your attempt
Correct Answer

B. (4,16,36,64)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (4,16,36,64) मिलते हैं। \(n^2\) को (4) से गुणा करें। / Putting (n=1,2,3,4) gives (4,16,36,64). Multiply \(n^2\) by (4).

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Question 25/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

कौन सा क्रम \(a_n=3^n-1\) से बने पहले चार पद दिखाता है?

Which sequence shows the first four terms of \(a_n=3^n-1\)?

Explanation opens after your attempt
Correct Answer

A. (2,8,26,80)

Explanation

Simple Explanation

\(3^1-1=2\), \(3^2-1=8\), \(3^3-1=26\), \(3^4-1=80\)। घात निकालकर (1) घटाएँ। / \(3^1-1=2\), \(3^2-1=8\), \(3^3-1=26\), and \(3^4-1=80\). Evaluate the power and subtract (1).

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Question 26/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,8,12,16,\ldots\) और \(7,11,15,19,\ldots\) के (7)वें पदों का अंतर क्या है?

What is the difference between the (7)th terms of \(4,8,12,16,\ldots\) and \(7,11,15,19,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

दोनों क्रमों का समान अंतर (4) है, इसलिए पदों का अंतर हमेशा (3) रहेगा। (7)वें पदों में भी यही अंतर है। / Both sequences have common difference (4), so the term difference always remains (3). The (7)th terms also differ by (3).

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Question 27/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(12,18,24,\ldots\) का (6)ठा पद और \(5,11,17,\ldots\) का (6)ठा पद किस प्रकार संबंधित हैं?

How are the (6)th term of \(12,18,24,\ldots\) and the (6)th term of \(5,11,17,\ldots\) related?

Explanation opens after your attempt
Correct Answer

A. पहला (7) अधिक हैThe first is greater by (7)

Explanation

Simple Explanation

दोनों क्रमों का अंतर (6) है और पहले पदों का अंतर (7) है। इसलिए (6)ठे पदों का अंतर भी (7) होगा। / Both sequences have difference (6), and the first terms differ by (7). So their (6)th terms also differ by (7).

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Question 28/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,9,14,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of \(4,9,14,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (90)

Explanation

Simple Explanation

पहले (6) पद (4,9,14,19,24,29) हैं। इनका योग (99) नहीं, (99) है इसलिए विकल्पों में सही मान नहीं है। / The first (6) terms are (4,9,14,19,24,29). Their sum is (99), so no listed option is correct.

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Question 29/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(60,54,48,\ldots\) के पहले (5) पदों का योग क्या है?

What is the sum of the first (5) terms of \(60,54,48,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (240)

Explanation

Simple Explanation

पहले (5) पद (60,54,48,42,36) हैं। इनका योग (240) है। / The first (5) terms are (60,54,48,42,36). Their sum is (240).

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Question 30/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(2,7,12,17,\ldots\) में कौन सा पद (47) है?

Which term is (47) in \(2,7,12,17,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Explanation

Simple Explanation

पहला पद (2) और अंतर (5) है। (2+(n-1)5=47) से (n=10) मिलता है। / The first term is (2) and the difference is (5). From (2+(n-1)5=47), (n=10).

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Question 31/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,10,14,18,\ldots\) में \(a_5+a_6\) का मान क्या है?

What is the value of \(a_5+a_6\) in \(6,10,14,18,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (46)

Explanation

Simple Explanation

\(a_5=22\) और \(a_6=26\) है। इसलिए \(a_5+a_6=48\), अतः विकल्प (D) सही है। / \(a_5=22\) and \(a_6=26\). Therefore \(a_5+a_6=48\), so option (D) is correct.

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Question 32/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(15,21,27,33,\ldots\) में \(a_6-a_3\) क्या है?

What is \(a_6-a_3\) in \(15,21,27,33,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (18)

Explanation

Simple Explanation

\(a_6=45\) और \(a_3=27\) है। इसलिए \(a_6-a_3=18\) है। / \(a_6=45\) and \(a_3=27\). Therefore \(a_6-a_3=18\).

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Question 33/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(10,14,18,22,\ldots\) में \(a_5\) और \(a_2\) का अंतर क्या है?

What is the difference between \(a_5\) and \(a_2\) in \(10,14,18,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (12)

Explanation

Simple Explanation

\(a_5=26\) और \(a_2=14\) है। उनका अंतर (26-14=12) है। / \(a_5=26\) and \(a_2=14\). Their difference is (26-14=12).

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Question 34/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=9\) और हर अगले पद में (5) जोड़ा जाता है, तो \(a_7\) क्या होगा?

If \(a_1=9\) and (5) is added to each next term, what is \(a_7\)?

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Correct Answer

C. (39)

Explanation

Simple Explanation

\(a_7=9+6\times5=39\) है। (7)वें पद तक पहुँचने के लिए (6) बार अंतर जोड़ा जाता है। / \(a_7=9+6\times5=39\). To reach the (7)th term, the difference is added (6) times.

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Question 35/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=72\) और हर अगले पद में (8) घटाया जाता है, तो \(a_6\) क्या होगा?

If \(a_1=72\) and (8) is subtracted for each next term, what is \(a_6\)?

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Correct Answer

B. (32)

Explanation

Simple Explanation

\(a_6=72-5\times8=32\) है। (6)ठे पद तक (5) बार घटाव होगा। / \(a_6=72-5\times8=32\). There are (5) subtractions before the (6)th term.

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Question 36/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,10,31,94,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (3) गुना और (1) जोड़ना है?

What is the next term in \(3,10,31,94,\ldots\) if the rule is triple the previous term and add (1)?

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Correct Answer

C. (283)

Explanation

Simple Explanation

नियम के अनुसार \(94\times3+1=283\) है। अंतिम पद पर दिया गया नियम लगाएँ। / By the rule, \(94\times3+1=283\). Apply the given rule to the last term.

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Question 37/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(64,31,14.5,6.25,\ldots\) में अगला पद क्या है यदि नियम पिछले पद को (2) से भाग देकर (1) घटाना है?

What is the next term in \(64,31,14.5,6.25,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?

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Correct Answer

A. (2.125)

Explanation

Simple Explanation

\(6.25\div2-1=2.125\) है। पहले भाग दें और फिर (1) घटाएँ। / \(6.25\div2-1=2.125\). Divide first and then subtract (1).

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Question 38/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(5,8,14,23,35,\ldots\) में अगला पद क्या है?

What is the next term in \(5,8,14,23,35,\ldots\)?

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Correct Answer

D. (50)

Explanation

Simple Explanation

अंतर (3,6,9,12) हैं, इसलिए अगला अंतर (15) होगा। (35+15=50) है। / The differences are (3,6,9,12), so the next difference is (15). (35+15=50).

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Question 39/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(150,140,120,90,50,\ldots\) में अगला पद क्या होगा?

What will be the next term in \(150,140,120,90,50,\ldots\)?

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Correct Answer

A. (0)

Explanation

Simple Explanation

घटाव (10,20,30,40) है, अगला घटाव (50) होगा। (50-50=0) है। / The subtractions are (10,20,30,40), so the next subtraction is (50). (50-50=0).

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Question 40/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(2,4,12,48,\ldots\) का अगला पद क्या है?

What is the next term of \(2,4,12,48,\ldots\)?

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Correct Answer

C. (240)

Explanation

Simple Explanation

यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा, इसलिए \(48\times5=240\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(48\times5=240\).

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Question 41/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,12,48,192,\ldots\) और \(5,20,80,320,\ldots\) के (4)थे पदों का अनुपात क्या है?

What is the ratio of the (4)th terms of \(3,12,48,192,\ldots\) and \(5,20,80,320,\ldots\)?

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Correct Answer

A. (3:5)

Explanation

Simple Explanation

चौथे पद (192) और (320) हैं। उनका अनुपात (192:320=3:5) है। / The fourth terms are (192) and (320). Their ratio is (192:320=3:5).

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

क्रम \(8,13,18,23,\ldots\) में पहले कितने पदों का योग (90) है?

How many first terms of \(8,13,18,23,\ldots\) have sum (90)?

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Correct Answer

B. (5)

Explanation

Simple Explanation

पहले (5) पद (8,13,18,23,28) हैं। उनका योग (90) है। / The first (5) terms are (8,13,18,23,28). Their sum is (90).

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Question 43/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,13,20,\ldots\) में कौन सा पद (41) से ठीक पहले आता है?

In \(6,13,20,\ldots\), which term comes just before (41)?

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Correct Answer

C. (34)

Explanation

Simple Explanation

क्रम (6,13,20,27,34,41) है। (41) से ठीक पहले (34) आता है। / The sequence is (6,13,20,27,34,41). The term just before (41) is (34).

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Question 44/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(160,80,40,20,\ldots\) में (5) से ठीक पहले कौन सा पद आता है?

In \(160,80,40,20,\ldots\), which term comes just before (5)?

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Correct Answer

B. (10)

Explanation

Simple Explanation

हर बार आधा हो रहा है। क्रम (160,80,40,20,10,5) है, इसलिए (5) से पहले (10) है। / Each term is halved. The sequence is (160,80,40,20,10,5), so (10) comes before (5).

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Question 45/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(11,15,19,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?

Which statement is correct for the (n)th term of \(11,15,19,\ldots\)?

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Correct Answer

A. यह (4n+7) हैIt is (4n+7)

Explanation

Simple Explanation

(n=1) पर (4(1)+7=11) और अंतर (4) मिलता है। इसलिए सही नियम (4n+7) है। / At (n=1), (4(1)+7=11), and the difference is (4). So the correct rule is (4n+7).

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

क्रम \(60,52,44,\ldots\) के (n)वें पद का सही नियम कौन सा है?

Which is the correct rule for the (n)th term of \(60,52,44,\ldots\)?

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Correct Answer

A. \(a_n=68-8n\)

Explanation

Simple Explanation

(n=1) रखने पर (68-8=60) मिलता है। यह हर बार (8) घटाने वाला नियम है। / Putting (n=1) gives (68-8=60). This rule decreases by (8) each time.

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Question 47/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=4\), \(a_2=9\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_5\) क्या होगा?

If \(a_1=4\), \(a_2=9\), and each next term is the sum of the previous two terms, what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (35)

Explanation

Simple Explanation

क्रम (4,9,13,22,35) बनेगा। इसलिए \(a_5=35\) है। / The sequence becomes (4,9,13,22,35). Therefore \(a_5=35\).

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Question 48/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि क्रम \(3,12,48,192,\ldots\) में \(a_n=768\) है, तो (n) क्या है?

If \(a_n=768\) in the sequence \(3,12,48,192,\ldots\), what is (n)?

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Correct Answer

B. (5)

Explanation

Simple Explanation

क्रम (3,12,48,192,768) है। (768) पाँचवाँ पद है, इसलिए (n=5)। / The sequence is (3,12,48,192,768). (768) is the fifth term, so (n=5).

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Question 49/50 Medium Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(2,6,14,30,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (2) गुना करके (2) जोड़ना है?

What is the next term in \(2,6,14,30,\ldots\) if the rule is double the previous term and add (2)?

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Correct Answer

C. (62)

Explanation

Simple Explanation

नियम के अनुसार \(30\times2+2=62\) है। अंतिम पद पर नियम लगाकर अगला पद निकालें। / By the rule, \(30\times2+2=62\). Apply the rule to the last term to get the next term.

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

क्रम \(5,12,21,32,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(5,12,21,32,\ldots\)?

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Correct Answer

B. (45)

Explanation

Simple Explanation

अंतर (7,9,11) हैं, इसलिए अगला अंतर (13) होगा। (32+13=45) है। / The differences are (7,9,11), so the next difference is (13). (32+13=45).

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