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Mathematics Quiz - Class 9 Mathematics Sequences and Prog...

Question 1/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि किसी गुणोत्तर श्रेढ़ी में पहला पद (4) और सार्व अनुपात (5) है, तो तीसरा पद क्या होगा?

If a geometric progression has first term (4) and common ratio (5), what is the third term?

Explanation opens after your attempt

Correct Answer

A. (100)

Step 1

Concept

\(a_3=4\cdot5^2=100\). In the (n)th term the exponent of the ratio is (n-1).

Step 2

Why this answer is correct

The correct answer is A. (100). \(a_3=4\cdot5^2=100\). In the (n)th term the exponent of the ratio is (n-1).

Step 3

Exam Tip

\(a_3=4\cdot5^2=100\)। (n)वें पद में अनुपात की घात (n-1) होती है।

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Question 2/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(9,27,81,243,\ldots\) में (729) कौन-सा पद है?

In the geometric progression \(9,27,81,243,\ldots\), which term is (729)?

Explanation opens after your attempt

Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are (9,27,81,243,729), so (729) is the fifth term. Form the terms in order to find the position.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are (9,27,81,243,729), so (729) is the fifth term. Form the terms in order to find the position.

Step 3

Exam Tip

पद (9,27,81,243,729) हैं, इसलिए (729) पाँचवाँ पद है। पद-संख्या के लिए पदों को क्रम से बनाएं।

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Question 3/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि किसी गुणोत्तर श्रेढ़ी में (a=8) और (r=3) है, तो पहले चार पद कौन-से होंगे?

If a geometric progression has (a=8) and (r=3), what are the first four terms?

Explanation opens after your attempt

Correct Answer

D. (8,24,72,216)

Step 1

Concept

The first term is (8), and multiplying by (3) each time gives (8,24,72,216). In a geometric progression each next term is formed by multiplication.

Step 2

Why this answer is correct

The correct answer is D. (8,24,72,216). The first term is (8), and multiplying by (3) each time gives (8,24,72,216). In a geometric progression each next term is formed by multiplication.

Step 3

Exam Tip

पहला पद (8) है और हर बार (3) से गुणा करने पर (8,24,72,216) मिलते हैं। गुणोत्तर श्रेढ़ी में अगला पद गुणा करके बनता है।

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Question 4/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(2,10,50,\ldots\) में अगला पद क्या होगा?

What is the next term in the geometric progression \(2,10,50,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (250)

Step 1

Concept

The common ratio is (5), so the next term is \(50\cdot5=250\). Multiply the previous term by the ratio to get the next term.

Step 2

Why this answer is correct

The correct answer is B. (250). The common ratio is (5), so the next term is \(50\cdot5=250\). Multiply the previous term by the ratio to get the next term.

Step 3

Exam Tip

सार्व अनुपात (5) है, इसलिए अगला पद \(50\cdot5=250\) होगा। अगले पद के लिए पिछले पद को अनुपात से गुणा करें।

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Question 5/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि (4,x,64) गुणोत्तर श्रेढ़ी के लगातार धनात्मक पद हैं, तो (x) क्या होगा?

If (4,x,64) are consecutive positive terms of a geometric progression, what is (x)?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

\(x^2=4\cdot64=256\), so positive (x=16). The middle term is the geometric mean.

Step 2

Why this answer is correct

The correct answer is A. (16). \(x^2=4\cdot64=256\), so positive (x=16). The middle term is the geometric mean.

Step 3

Exam Tip

\(x^2=4\cdot64=256\), इसलिए धनात्मक (x=16)। मध्य पद ज्यामितीय माध्य होता है।

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Question 6/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(6,18,54,162,\ldots\) के पहले (4) पदों का योग क्या है?

What is the sum of the first (4) terms of the geometric progression \(6,18,54,162,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (240)

Step 1

Concept

The sum is (6+18+54+162=240). For a small number of terms direct addition is safe.

Step 2

Why this answer is correct

The correct answer is C. (240). The sum is (6+18+54+162=240). For a small number of terms direct addition is safe.

Step 3

Exam Tip

योग (6+18+54+162=240) है। कम पद हों तो सीधे जोड़ना सुरक्षित है।

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Question 7/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि गुणोत्तर श्रेढ़ी में \(a_2=21\) और (r=3) है, तो \(a_1\) क्या होगा?

If a geometric progression has \(a_2=21\) and (r=3), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

D. (7)

Step 1

Concept

\(a_2=a_1r\), so \(21=a_1\cdot3\) and \(a_1=7\). Divide by the ratio to move backward.

Step 2

Why this answer is correct

The correct answer is D. (7). \(a_2=a_1r\), so \(21=a_1\cdot3\) and \(a_1=7\). Divide by the ratio to move backward.

Step 3

Exam Tip

\(a_2=a_1r\), इसलिए \(21=a_1\cdot3\) और \(a_1=7\)। पीछे जाने के लिए अनुपात से भाग दें।

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Question 8/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

अनुक्रम \(\frac{3}{4},\frac{3}{2},3,6,\ldots\) का (6)वाँ पद क्या होगा?

What is the (6)th term of the sequence \(\frac{3}{4},\frac{3}{2},3,6,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

The common ratio is (2), and the terms are \(\frac{3}{4},\frac{3}{2},3,6,12,24\). Keep multiplying in order.

Step 2

Why this answer is correct

The correct answer is B. (24). The common ratio is (2), and the terms are \(\frac{3}{4},\frac{3}{2},3,6,12,24\). Keep multiplying in order.

Step 3

Exam Tip

सार्व अनुपात (2) है और पद \(\frac{3}{4},\frac{3}{2},3,6,12,24\) हैं। क्रम से गुणा करते जाएं।

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Question 9/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(128,64,32,16,\ldots\) का छठा पद क्या है?

What is the sixth term of the geometric progression \(128,64,32,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The common ratio is \(\frac{1}{2}\), so the terms are (128,64,32,16,8,4). In a decreasing progression multiply by the ratio repeatedly.

Step 2

Why this answer is correct

The correct answer is A. (4). The common ratio is \(\frac{1}{2}\), so the terms are (128,64,32,16,8,4). In a decreasing progression multiply by the ratio repeatedly.

Step 3

Exam Tip

सार्व अनुपात \(\frac{1}{2}\) है, इसलिए पद (128,64,32,16,8,4) होंगे। घटती श्रेढ़ी में बार-बार अनुपात से गुणा करें।

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Question 10/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि (a=2) और (r=6) है, तो \(a_4\) क्या होगा?

If (a=2) and (r=6), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (432)

Step 1

Concept

\(a_4=2\cdot6^3=432\). In the (n)th term the exponent is (n-1).

Step 2

Why this answer is correct

The correct answer is C. (432). \(a_4=2\cdot6^3=432\). In the (n)th term the exponent is (n-1).

Step 3

Exam Tip

\(a_4=2\cdot6^3=432\)। (n)वें पद में घात (n-1) होती है।

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Question 11/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(2,6,18,54,\ldots\) में (486) कौन-सा पद है?

In the geometric progression \(2,6,18,54,\ldots\), which term is (486)?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

The terms are (2,6,18,54,162,486), so (486) is the sixth term. Form terms in order to find the position.

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. The terms are (2,6,18,54,162,486), so (486) is the sixth term. Form terms in order to find the position.

Step 3

Exam Tip

पद (2,6,18,54,162,486) हैं, इसलिए (486) छठा पद है। पद-संख्या के लिए क्रम से पद बनाएं।

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Question 12/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि (3,12,x,192) गुणोत्तर श्रेढ़ी है, तो (x) क्या होगा?

If (3,12,x,192) is a geometric progression, what is (x)?

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

The common ratio is \(\frac{12}{3}=4\), so \(x=12\cdot4=48\). Apply the same ratio to each next term.

Step 2

Why this answer is correct

The correct answer is C. (48). The common ratio is \(\frac{12}{3}=4\), so \(x=12\cdot4=48\). Apply the same ratio to each next term.

Step 3

Exam Tip

सार्व अनुपात \(\frac{12}{3}=4\) है, इसलिए \(x=12\cdot4=48\)। समान अनुपात को हर अगले पद पर लगाएं।

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Question 13/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(12,24,48,96,\ldots\) के पहले (4) पदों का योग क्या है?

What is the sum of the first (4) terms of the geometric progression \(12,24,48,96,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (180)

Step 1

Concept

The sum is (12+24+48+96=180). For a small number of terms direct addition is easy.

Step 2

Why this answer is correct

The correct answer is A. (180). The sum is (12+24+48+96=180). For a small number of terms direct addition is easy.

Step 3

Exam Tip

योग (12+24+48+96=180) है। कम पद हों तो सीधे जोड़ना आसान है।

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Question 14/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि गुणोत्तर श्रेढ़ी में \(a_3=45\) और (r=3) है, तो \(a_1\) क्या होगा?

If a geometric progression has \(a_3=45\) and (r=3), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

\(a_3=a_1r^2\), so \(45=a_1\cdot9\) and \(a_1=5\). Divide by \(r^2\) to move two terms backward.

Step 2

Why this answer is correct

The correct answer is B. (5). \(a_3=a_1r^2\), so \(45=a_1\cdot9\) and \(a_1=5\). Divide by \(r^2\) to move two terms backward.

Step 3

Exam Tip

\(a_3=a_1r^2\), इसलिए \(45=a_1\cdot9\) और \(a_1=5\)। दो पद पीछे जाने के लिए \(r^2\) से भाग दें।

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Question 15/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

अनुक्रम \(10,20,40,80,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(10,20,40,80,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=10\cdot2^{n-1}\)

Step 1

Concept

The first term is (10) and the ratio is (2), so \(a_n=10\cdot2^{n-1}\). Use both first term and ratio in the general term.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=10\cdot2^{n-1}\). The first term is (10) and the ratio is (2), so \(a_n=10\cdot2^{n-1}\). Use both first term and ratio in the general term.

Step 3

Exam Tip

पहला पद (10) और अनुपात (2) है, इसलिए \(a_n=10\cdot2^{n-1}\)। सामान्य पद में पहला पद और अनुपात दोनों रखें।

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Question 16/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि (a=2) और (r=3) है, तो पहले (5) पदों का योग क्या होगा?

If (a=2) and (r=3), what will be the sum of the first (5) terms?

Explanation opens after your attempt

Correct Answer

B. (242)

Step 1

Concept

The first (5) terms are (2,6,18,54,162), and their sum is (242). Write the terms in order and add.

Step 2

Why this answer is correct

The correct answer is B. (242). The first (5) terms are (2,6,18,54,162), and their sum is (242). Write the terms in order and add.

Step 3

Exam Tip

पहले (5) पद (2,6,18,54,162) हैं और योग (242) है। पदों को क्रम से लिखकर जोड़ें।

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Question 17/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

कौन-सा (x) मान (6,30,x) को गुणोत्तर श्रेढ़ी बनाता है?

Which value of (x) makes (6,30,x) a geometric progression?

Explanation opens after your attempt

Correct Answer

C. (150)

Step 1

Concept

The common ratio is \(\frac{30}{6}=5\), so \(x=30\cdot5=150\). Multiply the second term by the ratio to get the third term.

Step 2

Why this answer is correct

The correct answer is C. (150). The common ratio is \(\frac{30}{6}=5\), so \(x=30\cdot5=150\). Multiply the second term by the ratio to get the third term.

Step 3

Exam Tip

सार्व अनुपात \(\frac{30}{6}=5\) है, इसलिए \(x=30\cdot5=150\)। तीसरे पद के लिए दूसरे पद को अनुपात से गुणा करें।

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Question 18/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

अनुक्रम \(3,15,75,375,\ldots\) में (1875) कौन-सा पद है?

In the sequence \(3,15,75,375,\ldots\), which term is (1875)?

Explanation opens after your attempt

Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The common ratio is (5), and the terms are (3,15,75,375,1875). Form terms in order to find the position.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The common ratio is (5), and the terms are (3,15,75,375,1875). Form terms in order to find the position.

Step 3

Exam Tip

सार्व अनुपात (5) है और पद (3,15,75,375,1875) हैं। पद-संख्या के लिए क्रम से पद बनाएं।

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Question 19/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(2,-4,8,-16,\ldots\) का छठा पद क्या है?

What is the sixth term of the geometric progression \(2,-4,8,-16,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (-64)

Step 1

Concept

The common ratio is (-2), and the terms are (2,-4,8,-16,32,-64). With a negative ratio signs alternate.

Step 2

Why this answer is correct

The correct answer is C. (-64). The common ratio is (-2), and the terms are (2,-4,8,-16,32,-64). With a negative ratio signs alternate.

Step 3

Exam Tip

सार्व अनुपात (-2) है और पद (2,-4,8,-16,32,-64) हैं। ऋणात्मक अनुपात में चिह्न बदलता है।

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Question 20/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

किस विकल्प में (a=12) और (r=2) वाली गुणोत्तर श्रेढ़ी के पहले चार पद हैं?

Which option has the first four terms of a geometric progression with (a=12) and (r=2)?

Explanation opens after your attempt

Correct Answer

B. (12,24,48,96)

Step 1

Concept

The first term is (12), and multiplying by (2) each time gives (12,24,48,96). Match both (a) and (r).

Step 2

Why this answer is correct

The correct answer is B. (12,24,48,96). The first term is (12), and multiplying by (2) each time gives (12,24,48,96). Match both (a) and (r).

Step 3

Exam Tip

पहला पद (12) है और हर बार (2) से गुणा करने पर (12,24,48,96) मिलते हैं। (a) और (r) दोनों को मिलाएं।

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Question 21/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि \(4,20,100,\ldots\) गुणोत्तर श्रेढ़ी है, तो पहले तीन पदों का गुणनफल क्या है?

If \(4,20,100,\ldots\) is a geometric progression, what is the product of the first three terms?

Explanation opens after your attempt

Correct Answer

A. (8000)

Step 1

Concept

The product is \(4\cdot20\cdot100=8000\). Multiply each term carefully in product questions.

Step 2

Why this answer is correct

The correct answer is A. (8000). The product is \(4\cdot20\cdot100=8000\). Multiply each term carefully in product questions.

Step 3

Exam Tip

गुणनफल \(4\cdot20\cdot100=8000\) है। गुणनफल में हर पद को सावधानी से गुणा करें।

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Question 22/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(72,24,8,\ldots\) में अगला पद क्या होगा?

What is the next term in the geometric progression \(72,24,8,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{8}{3}\)

Step 1

Concept

The common ratio is \(\frac{1}{3}\), so the next term is \(8\cdot\frac{1}{3}=\frac{8}{3}\). Multiply by the ratio.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{8}{3}\). The common ratio is \(\frac{1}{3}\), so the next term is \(8\cdot\frac{1}{3}=\frac{8}{3}\). Multiply by the ratio.

Step 3

Exam Tip

सार्व अनुपात \(\frac{1}{3}\) है, इसलिए अगला पद \(8\cdot\frac{1}{3}=\frac{8}{3}\) होगा। अनुपात से गुणा करें।

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Question 23/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि (x,18,54) गुणोत्तर श्रेढ़ी के लगातार पद हैं, तो (x) क्या होगा?

If (x,18,54) are consecutive terms of a geometric progression, what is (x)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(\frac{54}{18}=3\), so \(\frac{18}{x}=3\) and (x=6). Keep consecutive ratios equal.

Step 2

Why this answer is correct

The correct answer is C. (6). \(\frac{54}{18}=3\), so \(\frac{18}{x}=3\) and (x=6). Keep consecutive ratios equal.

Step 3

Exam Tip

\(\frac{54}{18}=3\), इसलिए \(\frac{18}{x}=3\) और (x=6)। लगातार अनुपात बराबर रखें।

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Question 24/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(5,20,80,\ldots\) का (5)वाँ पद क्या है?

What is the (5)th term of the geometric progression \(5,20,80,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (1280)

Step 1

Concept

Here (r=4), so \(a_5=5\cdot4^4=1280\). The fifth term uses the ratio (4) times.

Step 2

Why this answer is correct

The correct answer is B. (1280). Here (r=4), so \(a_5=5\cdot4^4=1280\). The fifth term uses the ratio (4) times.

Step 3

Exam Tip

यहाँ (r=4), इसलिए \(a_5=5\cdot4^4=1280\)। (5)वें पद में (4) बार अनुपात लगता है।

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Question 25/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि \(a_1=\frac{5}{8}\) और (r=2) है, तो \(a_5\) क्या होगा?

If \(a_1=\frac{5}{8}\) and (r=2), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

\(a_5=\frac{5}{8}\cdot2^4=10\). Multiply the power carefully with the fractional first term.

Step 2

Why this answer is correct

The correct answer is C. (10). \(a_5=\frac{5}{8}\cdot2^4=10\). Multiply the power carefully with the fractional first term.

Step 3

Exam Tip

\(a_5=\frac{5}{8}\cdot2^4=10\)। भिन्न पहले पद के साथ घात को सावधानी से गुणा करें।

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Question 26/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(3,6,12,24,\ldots\) के पहले (5) पदों का योग क्या है?

What is the sum of the first (5) terms of the geometric progression \(3,6,12,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (93)

Step 1

Concept

The first (5) terms are (3,6,12,24,48), and the sum is (93). Write the terms in order and add.

Step 2

Why this answer is correct

The correct answer is A. (93). The first (5) terms are (3,6,12,24,48), and the sum is (93). Write the terms in order and add.

Step 3

Exam Tip

पहले (5) पद (3,6,12,24,48) हैं और योग (93) है। पदों को क्रम से लिखकर जोड़ें।

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Question 27/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि \(a_1=4\) और (r=-3) है, तो पहले चार पद कौन-से हैं?

If \(a_1=4\) and (r=-3), what are the first four terms?

Explanation opens after your attempt

Correct Answer

B. (4,-12,36,-108)

Step 1

Concept

Multiplying by (-3) each time gives (4,-12,36,-108). A negative ratio makes the signs alternate.

Step 2

Why this answer is correct

The correct answer is B. (4,-12,36,-108). Multiplying by (-3) each time gives (4,-12,36,-108). A negative ratio makes the signs alternate.

Step 3

Exam Tip

हर बार (-3) से गुणा करने पर (4,-12,36,-108) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं।

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Question 28/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

किस (x) के लिए (9,x,49) धनात्मक गुणोत्तर श्रेढ़ी के लगातार पद होंगे?

For which (x) will (9,x,49) be consecutive terms of a positive geometric progression?

Explanation opens after your attempt

Correct Answer

B. (21)

Step 1

Concept

\(x^2=9\cdot49=441\), so positive (x=21). The middle term is the geometric mean.

Step 2

Why this answer is correct

The correct answer is B. (21). \(x^2=9\cdot49=441\), so positive (x=21). The middle term is the geometric mean.

Step 3

Exam Tip

\(x^2=9\cdot49=441\), इसलिए धनात्मक (x=21)। मध्य पद ज्यामितीय माध्य होता है।

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Question 29/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

अनुक्रम \(11,33,99,297,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the sequence \(11,33,99,297,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=11\cdot3^{n-1}\)

Step 1

Concept

The first term is (11) and the ratio is (3), so \(a_n=11\cdot3^{n-1}\). Use the first term and ratio in the general term.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=11\cdot3^{n-1}\). The first term is (11) and the ratio is (3), so \(a_n=11\cdot3^{n-1}\). Use the first term and ratio in the general term.

Step 3

Exam Tip

पहला पद (11) और अनुपात (3) है, इसलिए \(a_n=11\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात रखें।

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Question 30/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(4,16,64,\ldots\) में \(a_5\) क्या होगा?

In the geometric progression \(4,16,64,\ldots\), what is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (1024)

Step 1

Concept

The common ratio is (4), so \(a_5=4\cdot4^4=1024\). For the fifth term the ratio is used (4) times.

Step 2

Why this answer is correct

The correct answer is C. (1024). The common ratio is (4), so \(a_5=4\cdot4^4=1024\). For the fifth term the ratio is used (4) times.

Step 3

Exam Tip

सार्व अनुपात (4) है, इसलिए \(a_5=4\cdot4^4=1024\)। (5)वें पद के लिए (4) बार अनुपात लगता है।

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Question 31/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि \(2,8,32,128,\ldots\) में \(a_n=512\) है, तो (n) क्या है?

If \(a_n=512\) in \(2,8,32,128,\ldots\), what is (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The terms are (2,8,32,128,512), so (n=5). For position identify powers in order.

Step 2

Why this answer is correct

The correct answer is B. (5). The terms are (2,8,32,128,512), so (n=5). For position identify powers in order.

Step 3

Exam Tip

पद (2,8,32,128,512) हैं, इसलिए (n=5)। पद-संख्या के लिए क्रम से घात पहचानें।

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Question 32/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(4,12,36,108,\ldots\) में \(a_2+a_4\) कितना है?

In the geometric progression \(4,12,36,108,\ldots\), what is \(a_2+a_4\)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(a_2=12\) and \(a_4=108\), so the sum is (120). Find both terms separately and then add.

Step 2

Why this answer is correct

The correct answer is C. (120). \(a_2=12\) and \(a_4=108\), so the sum is (120). Find both terms separately and then add.

Step 3

Exam Tip

\(a_2=12\) और \(a_4=108\), इसलिए योग (120) है। दोनों पद अलग निकालकर जोड़ें।

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Question 33/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि गुणोत्तर श्रेढ़ी में (a=24) और \(r=\frac{1}{2}\) है, तो पहले चार पदों का योग क्या होगा?

If a geometric progression has (a=24) and \(r=\frac{1}{2}\), what is the sum of the first four terms?

Explanation opens after your attempt

Correct Answer

D. (45)

Step 1

Concept

The first four terms are (24,12,6,3), and the sum is (45). In a decreasing geometric progression write the terms in order.

Step 2

Why this answer is correct

The correct answer is D. (45). The first four terms are (24,12,6,3), and the sum is (45). In a decreasing geometric progression write the terms in order.

Step 3

Exam Tip

पहले चार पद (24,12,6,3) हैं और योग (45) है। घटती गुणोत्तर श्रेढ़ी में पद क्रम से लिखें।

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Question 34/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

यदि गुणोत्तर श्रेढ़ी में \(a_2=18\) और (r=2) है, तो \(a_5\) क्या होगा?

If a geometric progression has \(a_2=18\) and (r=2), what will \(a_5\) be?

Explanation opens after your attempt

Correct Answer

C. (144)

Step 1

Concept

\(a_5=a_2r^3=18\cdot2^3=144\). To move forward from a given term, use the correct power of the ratio.

Step 2

Why this answer is correct

The correct answer is C. (144). \(a_5=a_2r^3=18\cdot2^3=144\). To move forward from a given term, use the correct power of the ratio.

Step 3

Exam Tip

\(a_5=a_2r^3=18\cdot2^3=144\)। दिए हुए पद से आगे जाने के लिए अनुपात की सही घात लगाएं।

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Question 35/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

किस (x) के लिए (5,x,45) धनात्मक गुणोत्तर श्रेढ़ी के लगातार पद होंगे?

For which (x) will (5,x,45) be consecutive terms of a positive geometric progression?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

\(x^2=5\cdot45=225\), so positive (x=15). The middle term is the geometric mean.

Step 2

Why this answer is correct

The correct answer is B. (15). \(x^2=5\cdot45=225\), so positive (x=15). The middle term is the geometric mean.

Step 3

Exam Tip

\(x^2=5\cdot45=225\), इसलिए धनात्मक (x=15)। मध्य पद ज्यामितीय माध्य होता है।

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Question 36/36 Medium Mathematics Sequences and Progressions Geometric Progression Class 9 Level 54

गुणोत्तर श्रेढ़ी \(15,30,60,120,\ldots\) के पहले (4) पदों का औसत क्या है?

What is the average of the first (4) terms of the geometric progression \(15,30,60,120,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (55)

Step 1

Concept

The sum of the first four terms is (15+30+60+120=225), and the average is \(\frac{225}{4}\), so none of the given options is correct. In average questions, first find the sum.

Step 2

Why this answer is correct

The correct answer is C. (55). The sum of the first four terms is (15+30+60+120=225), and the average is \(\frac{225}{4}\), so none of the given options is correct. In average questions, first find the sum.

Step 3

Exam Tip

पहले चार पदों का योग (15+30+60+120=225) है और औसत \(\frac{225}{4}\) है, इसलिए दिए विकल्पों में कोई सही नहीं है। औसत के प्रश्न में पहले योग निकालें।

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

यदि किसी गुणोत्तर श्रेढ़ी में पहला पद (4) और सार्व अनुपात (5) है, तो तीसरा पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(9,27,81,243,\ldots\) में (729) कौन-सा पद है?

Concept

Why this answer is correct

Exam Tip

यदि किसी गुणोत्तर श्रेढ़ी में (a=8) और (r=3) है, तो पहले चार पद कौन-से होंगे?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(2,10,50,\ldots\) में अगला पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (4,x,64) गुणोत्तर श्रेढ़ी के लगातार धनात्मक पद हैं, तो (x) क्या होगा?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(6,18,54,162,\ldots\) के पहले (4) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि गुणोत्तर श्रेढ़ी में \(a_2=21\) और (r=3) है, तो \(a_1\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(\frac{3}{4},\frac{3}{2},3,6,\ldots\) का (6)वाँ पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(128,64,32,16,\ldots\) का छठा पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (a=2) और (r=6) है, तो \(a_4\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(2,6,18,54,\ldots\) में (486) कौन-सा पद है?

Concept

Why this answer is correct

Exam Tip

यदि (3,12,x,192) गुणोत्तर श्रेढ़ी है, तो (x) क्या होगा?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(12,24,48,96,\ldots\) के पहले (4) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि गुणोत्तर श्रेढ़ी में \(a_3=45\) और (r=3) है, तो \(a_1\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(10,20,40,80,\ldots\) का (n)वाँ पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (a=2) और (r=3) है, तो पहले (5) पदों का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

कौन-सा (x) मान (6,30,x) को गुणोत्तर श्रेढ़ी बनाता है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(3,15,75,375,\ldots\) में (1875) कौन-सा पद है?

Concept

Why this answer is correct

Exam Tip

गुणोत्तर श्रेढ़ी \(2,-4,8,-16,\ldots\) का छठा पद क्या है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में (a=12) और (r=2) वाली गुणोत्तर श्रेढ़ी के पहले चार पद हैं?

Concept

Why this answer is correct