अनुक्रम \(6,18,54,162,\ldots\) में सामान्य अनुपात क्या है?
What is the common ratio in the sequence \(6,18,54,162,\ldots\)?
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A (2)
B (4)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
The ratio of consecutive terms is \(18\div6=3\). In exams divide the second term by the first term.
Step 2
Why this answer is correct
The correct answer is C. (3). The ratio of consecutive terms is \(18\div6=3\). In exams divide the second term by the first term.
Step 3
Exam Tip
लगातार पदों का अनुपात \(18\div6=3\) है। परीक्षा में दूसरे पद को पहले पद से भाग दें।
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गुणोत्तर श्रेणी \(4,16,64,256,\ldots\) का अगला पद क्या होगा?
What will be the next term of the geometric progression \(4,16,64,256,\ldots\)?
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A (512)
B (768)
C (1024)
D (2048)
Explanation opens after your attempt
Step 1
Concept
Each term is multiplied by (4) so the next term is \(256\times4=1024\). In exams first identify the common ratio.
Step 2
Why this answer is correct
The correct answer is C. (1024). Each term is multiplied by (4) so the next term is \(256\times4=1024\). In exams first identify the common ratio.
Step 3
Exam Tip
हर बार (4) से गुणा हो रहा है इसलिए अगला पद \(256\times4=1024\) है। परीक्षा में पहले सामान्य अनुपात पहचानें।
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यदि गुणोत्तर श्रेणी में पहला पद (7) और सामान्य अनुपात (4) है तो दूसरा पद क्या होगा?
If a geometric progression has first term (7) and common ratio (4) what is the second term?
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A (11)
B (21)
C (28)
D (32)
Explanation opens after your attempt
Step 1
Concept
The second term is \(7\times4=28\). In exams multiply by the common ratio to get the next term.
Step 2
Why this answer is correct
The correct answer is C. (28). The second term is \(7\times4=28\). In exams multiply by the common ratio to get the next term.
Step 3
Exam Tip
दूसरा पद \(7\times4=28\) होगा। परीक्षा में अगले पद के लिए सामान्य अनुपात से गुणा करें।
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अनुक्रम \(243,81,27,9,\ldots\) में सामान्य अनुपात क्या है?
What is the common ratio in the sequence \(243,81,27,9,\ldots\)?
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A (3)
B \(\frac{1}{3}\)
C \(\frac{1}{9}\)
D (9)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
The ratio of consecutive terms is \(81\div243=\frac{1}{3}\). In exams a decreasing geometric progression can have a fractional ratio.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). The ratio of consecutive terms is \(81\div243=\frac{1}{3}\). In exams a decreasing geometric progression can have a fractional ratio.
Step 3
Exam Tip
लगातार पदों का अनुपात \(81\div243=\frac{1}{3}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में अनुपात भिन्न हो सकता है।
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क्या अनुक्रम \(5,25,125,625,\ldots\) एक गुणोत्तर श्रेणी है?
Is the sequence \(5,25,125,625,\ldots\) a geometric progression?
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A हाँ सामान्य अनुपात (5) है / Yes common ratio is (5)
B हाँ सामान्य अनुपात (25) है / Yes common ratio is (25)
C नहीं अनुपात समान नहीं है / No ratios are not equal
D नहीं पद घट रहे हैं / No terms are decreasing
Explanation opens after your attempt
Correct Answer
A. हाँ सामान्य अनुपात (5) है / Yes common ratio is (5)
Step 1
Concept
All consecutive terms have ratio (5). In exams check equal ratios for a geometric progression.
Step 2
Why this answer is correct
The correct answer is A. हाँ सामान्य अनुपात (5) है / Yes common ratio is (5). All consecutive terms have ratio (5). In exams check equal ratios for a geometric progression.
Step 3
Exam Tip
सभी लगातार पदों का अनुपात (5) है। परीक्षा में गुणोत्तर श्रेणी के लिए समान अनुपात जाँचें।
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अनुक्रम \(2,6,12,20,\ldots\) गुणोत्तर श्रेणी क्यों नहीं है?
Why is the sequence \(2,6,12,20,\ldots\) not a geometric progression?
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A पहला पद (2) है / First term is (2)
B पद बढ़ रहे हैं / Terms are increasing
C अनुपात समान नहीं हैं / Ratios are not equal
D सभी पद सम हैं / All terms are even
Explanation opens after your attempt
Correct Answer
C. अनुपात समान नहीं हैं / Ratios are not equal
Step 1
Concept
The ratios \(6\div2=3\) and \(12\div6=2\) are not equal. In exams check consecutive ratios.
Step 2
Why this answer is correct
The correct answer is C. अनुपात समान नहीं हैं / Ratios are not equal. The ratios \(6\div2=3\) and \(12\div6=2\) are not equal. In exams check consecutive ratios.
Step 3
Exam Tip
अनुपात \(6\div2=3\) और \(12\div6=2\) समान नहीं हैं। परीक्षा में लगातार अनुपात जाँचें।
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गुणोत्तर श्रेणी \(12,36,108,324,\ldots\) में पहला पद क्या है?
What is the first term in the geometric progression \(12,36,108,324,\ldots\)?
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A (3)
B (12)
C (36)
D (108)
Explanation opens after your attempt
Step 1
Concept
The first written term of the sequence is (12). In exams take the first term (a) directly from the sequence.
Step 2
Why this answer is correct
The correct answer is B. (12). The first written term of the sequence is (12). In exams take the first term (a) directly from the sequence.
Step 3
Exam Tip
अनुक्रम का पहला लिखा हुआ पद (12) है। परीक्षा में पहला पद (a) सीधे पहले पद से लें।
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यदि (a=2) और (r=6) है तो गुणोत्तर श्रेणी का तीसरा पद क्या होगा?
If (a=2) and (r=6) what is the third term of the geometric progression?
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A (24)
B (36)
C (72)
D (108)
Explanation opens after your attempt
Step 1
Concept
The third term is \(ar^2=2\times6^2=72\). In exams use the square of the ratio for the third term.
Step 2
Why this answer is correct
The correct answer is C. (72). The third term is \(ar^2=2\times6^2=72\). In exams use the square of the ratio for the third term.
Step 3
Exam Tip
तीसरा पद \(ar^2=2\times6^2=72\) है। परीक्षा में तीसरे पद के लिए अनुपात का वर्ग लगाएँ।
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गुणोत्तर श्रेणी \(128,64,32,16,\ldots\) का अगला पद क्या होगा?
What is the next term of the geometric progression \(128,64,32,16,\ldots\)?
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A (4)
B (8)
C (12)
D (10)
Explanation opens after your attempt
Step 1
Concept
Each term is multiplied by \(\frac{1}{2}\) so the next term is \(16\times\frac{1}{2}=8\). In exams identify fractional ratios in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is B. (8). Each term is multiplied by \(\frac{1}{2}\) so the next term is \(16\times\frac{1}{2}=8\). In exams identify fractional ratios in decreasing sequences.
Step 3
Exam Tip
हर बार \(\frac{1}{2}\) से गुणा हो रहा है इसलिए अगला पद \(16\times\frac{1}{2}=8\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात पहचानें।
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गुणोत्तर श्रेणी \(4,12,36,108,\ldots\) में पाँचवाँ पद क्या है?
What is the fifth term in the geometric progression \(4,12,36,108,\ldots\)?
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A (216)
B (324)
C (432)
D (648)
Explanation opens after your attempt
Step 1
Concept
The common ratio is (3) so the fifth term is \(108\times3=324\). In exams multiply the last known term by the ratio.
Step 2
Why this answer is correct
The correct answer is B. (324). The common ratio is (3) so the fifth term is \(108\times3=324\). In exams multiply the last known term by the ratio.
Step 3
Exam Tip
सामान्य अनुपात (3) है इसलिए पाँचवाँ पद \(108\times3=324\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें।
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यदि गुणोत्तर श्रेणी \(6,,\Box,,54,162,\ldots\) है तो रिक्त स्थान में कौन-सा पद होगा?
If \(6,,\Box,,54,162,\ldots\) is a geometric progression what term fills the blank?
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A (12)
B (18)
C (24)
D (27)
Explanation opens after your attempt
Step 1
Concept
The ratio of (54) and (162) is (3) so the missing term is \(54\div3=18\). In exams apply the ratio backward too.
Step 2
Why this answer is correct
The correct answer is B. (18). The ratio of (54) and (162) is (3) so the missing term is \(54\div3=18\). In exams apply the ratio backward too.
Step 3
Exam Tip
(54) और (162) का अनुपात (3) है इसलिए रिक्त पद \(54\div3=18\) है। परीक्षा में पीछे की ओर भी अनुपात लगाएँ।
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गुणोत्तर श्रेणी \(5,20,80,320,\ldots\) का सामान्य पद क्या है?
What is the general term of the geometric progression \(5,20,80,320,\ldots\)?
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A \(a_n=5\cdot4^{n-1}\)
B \(a_n=4\cdot5^{n-1}\)
C \(a_n=5n\)
D \(a_n=20n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5\cdot4^{n-1}\)
Step 1
Concept
The first term is (5) and the ratio is (4) so \(a_n=5\cdot4^{n-1}\). In exams use \(a_n=ar^{n-1}\).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5\cdot4^{n-1}\). The first term is (5) and the ratio is (4) so \(a_n=5\cdot4^{n-1}\). In exams use \(a_n=ar^{n-1}\).
Step 3
Exam Tip
पहला पद (5) और अनुपात (4) है इसलिए \(a_n=5\cdot4^{n-1}\) है। परीक्षा में \(a_n=ar^{n-1}\) लगाएँ।
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यदि \(a_n=6^n\) है तो \(a_2\) का मान क्या होगा?
If \(a_n=6^n\) what is the value of \(a_2\)?
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A (12)
B (18)
C (36)
D (216)
Explanation opens after your attempt
Step 1
Concept
\(a_2=6^2=36\). In exams calculate the power carefully.
Step 2
Why this answer is correct
The correct answer is C. (36). \(a_2=6^2=36\). In exams calculate the power carefully.
Step 3
Exam Tip
\(a_2=6^2=36\) है। परीक्षा में घात का मान ध्यान से निकालें।
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गुणोत्तर श्रेणी \(8,40,200,1000,\ldots\) का सामान्य पद कौन-सा है?
Which is the general term of the geometric progression \(8,40,200,1000,\ldots\)?
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A \(a_n=8n\)
B \(a_n=8\cdot5^{n-1}\)
C \(a_n=5\cdot8^{n-1}\)
D \(a_n=40n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=8\cdot5^{n-1}\)
Step 1
Concept
The first term is (8) and the ratio is (5) so \(a_n=8\cdot5^{n-1}\). In exams use \(a_n=ar^{n-1}\).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=8\cdot5^{n-1}\). The first term is (8) and the ratio is (5) so \(a_n=8\cdot5^{n-1}\). In exams use \(a_n=ar^{n-1}\).
Step 3
Exam Tip
पहला पद (8) और अनुपात (5) है इसलिए \(a_n=8\cdot5^{n-1}\) है। परीक्षा में \(a_n=ar^{n-1}\) का प्रयोग करें।
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यदि गुणोत्तर श्रेणी का पहला पद (54) और सामान्य अनुपात \(\frac{1}{3}\) है तो दूसरा पद क्या होगा?
If the first term of a geometric progression is (54) and common ratio is \(\frac{1}{3}\) what is the second term?
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A (9)
B (18)
C (27)
D (162)
Explanation opens after your attempt
Step 1
Concept
The second term is \(54\times\frac{1}{3}=18\). In exams multiply carefully by a fractional ratio.
Step 2
Why this answer is correct
The correct answer is B. (18). The second term is \(54\times\frac{1}{3}=18\). In exams multiply carefully by a fractional ratio.
Step 3
Exam Tip
दूसरा पद \(54\times\frac{1}{3}=18\) है। परीक्षा में भिन्न अनुपात से सावधानी से गुणा करें।
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अनुक्रम \(2,5,10,17,\ldots\) गुणोत्तर श्रेणी क्यों नहीं है?
Why is the sequence \(2,5,10,17,\ldots\) not a geometric progression?
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A पहला पद (2) है / First term is (2)
B पद बढ़ रहे हैं / Terms are increasing
C लगातार अनुपात समान नहीं हैं / Consecutive ratios are not equal
D सभी पद धनात्मक हैं / All terms are positive
Explanation opens after your attempt
Correct Answer
C. लगातार अनुपात समान नहीं हैं / Consecutive ratios are not equal
Step 1
Concept
The ratios \(5\div2=\frac{5}{2}\) and \(10\div5=2\) are not equal. In exams equal ratio is necessary for a geometric progression.
Step 2
Why this answer is correct
The correct answer is C. लगातार अनुपात समान नहीं हैं / Consecutive ratios are not equal. The ratios \(5\div2=\frac{5}{2}\) and \(10\div5=2\) are not equal. In exams equal ratio is necessary for a geometric progression.
Step 3
Exam Tip
अनुपात \(5\div2=\frac{5}{2}\) और \(10\div5=2\) समान नहीं हैं। परीक्षा में गुणोत्तर श्रेणी के लिए समान अनुपात जरूरी है।
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गुणोत्तर श्रेणी \(15,45,135,405,\ldots\) में (r) का मान क्या है?
What is the value of (r) in the geometric progression \(15,45,135,405,\ldots\)?
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A (2)
B (3)
C (5)
D (15)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(r=45\div15=3\). In exams divide the second term by the first term for (r).
Step 2
Why this answer is correct
The correct answer is B. (3). The common ratio is \(r=45\div15=3\). In exams divide the second term by the first term for (r).
Step 3
Exam Tip
सामान्य अनुपात \(r=45\div15=3\) है। परीक्षा में (r) के लिए दूसरे पद को पहले पद से भाग दें।
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यदि (a=8) और (r=2) है तो गुणोत्तर श्रेणी का चौथा पद क्या होगा?
If (a=8) and (r=2) what is the fourth term of the geometric progression?
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A (32)
B (48)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
The fourth term is \(ar^3=8\times2^3=64\). In exams use \(r^3\) for the fourth term.
Step 2
Why this answer is correct
The correct answer is C. (64). The fourth term is \(ar^3=8\times2^3=64\). In exams use \(r^3\) for the fourth term.
Step 3
Exam Tip
चौथा पद \(ar^3=8\times2^3=64\) है। परीक्षा में चौथे पद के लिए \(r^3\) लगाएँ।
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गुणोत्तर श्रेणी \(144,72,36,18,\ldots\) में पाँचवाँ पद क्या है?
What is the fifth term in the geometric progression \(144,72,36,18,\ldots\)?
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A (6)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(\frac{1}{2}\) so the fifth term is \(18\times\frac{1}{2}=9\). In exams simplify fractions.
Step 2
Why this answer is correct
The correct answer is B. (9). The common ratio is \(\frac{1}{2}\) so the fifth term is \(18\times\frac{1}{2}=9\). In exams simplify fractions.
Step 3
Exam Tip
सामान्य अनुपात \(\frac{1}{2}\) है इसलिए पाँचवाँ पद \(18\times\frac{1}{2}=9\) है। परीक्षा में भिन्नों को सरल करें।
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गुणोत्तर श्रेणी \(5,15,45,135,\ldots\) में (405) कौन-सा पद है?
In the geometric progression \(5,15,45,135,\ldots\) which term is (405)?
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A चौथा पद / (4)th term
B पाँचवाँ पद / (5)th term
C छठा पद / (6)th term
D सातवाँ पद / (7)th term
Explanation opens after your attempt
Correct Answer
B. पाँचवाँ पद / (5)th term
Step 1
Concept
The terms are (5,15,45,135,405) so (405) is the fifth term. In exams list small terms in order to check.
Step 2
Why this answer is correct
The correct answer is B. पाँचवाँ पद / (5)th term. The terms are (5,15,45,135,405) so (405) is the fifth term. In exams list small terms in order to check.
Step 3
Exam Tip
पद (5,15,45,135,405) हैं इसलिए (405) पाँचवाँ पद है। परीक्षा में छोटे पदों को क्रम से लिखकर जाँचें।
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यदि \(a_n=6\cdot2^{n-1}\) है तो यह पहले तीन पद कौन-से देता है?
If \(a_n=6\cdot2^{n-1}\) what first three terms does it give?
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A (6,12,24)
B (2,4,8)
C (12,24,48)
D (6,8,10)
Explanation opens after your attempt
Correct Answer
A. (6,12,24)
Step 1
Concept
Putting (n=1,2,3) gives (6,12,24). In exams apply the exponent (n-1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (6,12,24). Putting (n=1,2,3) gives (6,12,24). In exams apply the exponent (n-1) carefully.
Step 3
Exam Tip
(n=1,2,3) रखने पर (6,12,24) मिलते हैं। परीक्षा में (n-1) वाले घातांक को ध्यान से लगाएँ।
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गुणोत्तर श्रेणी \(7,28,112,448,\ldots\) का सामान्य पद क्या है?
What is the general term of the geometric progression \(7,28,112,448,\ldots\)?
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A \(a_n=7\cdot4^{n-1}\)
B \(a_n=7n\)
C \(a_n=4\cdot7^{n-1}\)
D \(a_n=28n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7\cdot4^{n-1}\)
Step 1
Concept
The first term is (7) and the ratio is (4) so \(a_n=7\cdot4^{n-1}\). In exams match both the first term and the ratio.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7\cdot4^{n-1}\). The first term is (7) and the ratio is (4) so \(a_n=7\cdot4^{n-1}\). In exams match both the first term and the ratio.
Step 3
Exam Tip
पहला पद (7) और अनुपात (4) है इसलिए \(a_n=7\cdot4^{n-1}\) है। परीक्षा में पहला पद और अनुपात दोनों मिलाएँ।
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यदि गुणोत्तर श्रेणी \(4,20,100,\Box,\ldots\) है तो रिक्त स्थान में कौन-सा पद होगा?
If \(4,20,100,\Box,\ldots\) is a geometric progression what term fills the blank?
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A (300)
B (400)
C (500)
D (600)
Explanation opens after your attempt
Step 1
Concept
The common ratio is (5) so the missing term is \(100\times5=500\). In exams continue the same ratio.
Step 2
Why this answer is correct
The correct answer is C. (500). The common ratio is (5) so the missing term is \(100\times5=500\). In exams continue the same ratio.
Step 3
Exam Tip
सामान्य अनुपात (5) है इसलिए रिक्त पद \(100\times5=500\) है। परीक्षा में समान अनुपात जारी रखें।
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गुणोत्तर श्रेणी \(72,24,8,\frac{8}{3},\ldots\) में सामान्य अनुपात क्या है?
What is the common ratio in the geometric progression \(72,24,8,\frac{8}{3},\ldots\)?
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A (3)
B \(\frac{1}{3}\)
C (6)
D \(\frac{1}{6}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
The ratio of consecutive terms is \(24\div72=\frac{1}{3}\). In exams write the fractional ratio for a decreasing geometric progression.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). The ratio of consecutive terms is \(24\div72=\frac{1}{3}\). In exams write the fractional ratio for a decreasing geometric progression.
Step 3
Exam Tip
लगातार पदों का अनुपात \(24\div72=\frac{1}{3}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में भिन्न अनुपात लिखें।
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गुणोत्तर श्रेणी \(2,8,32,128,\ldots\) में छठा पद क्या होगा?
What will be the sixth term in the geometric progression \(2,8,32,128,\ldots\)?
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A (256)
B (512)
C (1024)
D (2048)
Explanation opens after your attempt
Step 1
Concept
After the fourth term (128) the fifth is (512) and the sixth is (2048). In exams include the first term while counting.
Step 2
Why this answer is correct
The correct answer is D. (2048). After the fourth term (128) the fifth is (512) and the sixth is (2048). In exams include the first term while counting.
Step 3
Exam Tip
चौथे पद (128) के बाद पाँचवाँ (512) और छठा (2048) है। परीक्षा में पद संख्या गिनते समय पहला पद शामिल करें।
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क्या \(14,42,126,378,\ldots\) गुणोत्तर श्रेणी है?
Is \(14,42,126,378,\ldots\) a geometric progression?
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A हाँ सामान्य अनुपात (3) है / Yes common ratio is (3)
B हाँ सामान्य अनुपात (14) है / Yes common ratio is (14)
C नहीं पद समान नहीं हैं / No terms are not equal
D नहीं यह घटती श्रेणी है / No it is decreasing
Explanation opens after your attempt
Correct Answer
A. हाँ सामान्य अनुपात (3) है / Yes common ratio is (3)
Step 1
Concept
Each consecutive term has ratio (3). In exams if equal ratio appears treat it as a geometric progression.
Step 2
Why this answer is correct
The correct answer is A. हाँ सामान्य अनुपात (3) है / Yes common ratio is (3). Each consecutive term has ratio (3). In exams if equal ratio appears treat it as a geometric progression.
Step 3
Exam Tip
हर लगातार पद का अनुपात (3) है। परीक्षा में समान अनुपात दिखे तो गुणोत्तर श्रेणी मानें।
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यदि (a=4) और (r=7) है तो पहले चार पद कौन-से होंगे?
If (a=4) and (r=7) what are the first four terms?
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A (4,7,28,196)
B (4,28,196,1372)
C (7,28,196,1372)
D (4,11,18,25)
Explanation opens after your attempt
Correct Answer
B. (4,28,196,1372)
Step 1
Concept
Multiplying by (7) each time gives (4,28,196,1372). In exams do not change the first term.
Step 2
Why this answer is correct
The correct answer is B. (4,28,196,1372). Multiplying by (7) each time gives (4,28,196,1372). In exams do not change the first term.
Step 3
Exam Tip
हर बार (7) से गुणा करने पर (4,28,196,1372) मिलते हैं। परीक्षा में पहला पद न बदलें।
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गुणोत्तर श्रेणी \(100,20,4,\frac{4}{5},\ldots\) का सामान्य पद कौन-सा है?
Which is the general term of the geometric progression \(100,20,4,\frac{4}{5},\ldots\)?
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A \(a_n=100\cdot5^{n-1}\)
B \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\)
C \(a_n=100-n\)
D \(a_n=20n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\)
Step 1
Concept
The first term is (100) and the ratio is \(\frac{1}{5}\) so \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\). In exams use the fractional ratio in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\). The first term is (100) and the ratio is \(\frac{1}{5}\) so \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\). In exams use the fractional ratio in a decreasing sequence.
Step 3
Exam Tip
पहला पद (100) और अनुपात \(\frac{1}{5}) है इसलिए \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात लगाएँ।
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यदि \(a_n=64\cdot\left(\frac{1}{2}\right)^{n-1}\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=64\cdot\left(\frac{1}{2}\right)^{n-1}\) what is the value of \(a_5\)?
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(a_5=64\cdot\left(\frac{1}{2}\right)^4=4\). In exams keep the exponent (n-1) correct.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_5=64\cdot\left(\frac{1}{2}\right)^4=4\). In exams keep the exponent (n-1) correct.
Step 3
Exam Tip
\(a_5=64\cdot\left(\frac{1}{2}\right)^4=4\) है। परीक्षा में (n-1) वाले घातांक को सही रखें।
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गुणोत्तर श्रेणी \(3,18,108,648,\ldots\) में (a) और (r) क्या हैं?
What are (a) and (r) in the geometric progression \(3,18,108,648,\ldots\)?
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A (a=3,r=6)
B (a=6,r=3)
C (a=3,r=18)
D (a=18,r=6)
Explanation opens after your attempt
Correct Answer
A. (a=3,r=6)
Step 1
Concept
The first term is (3) and the ratio is \(18\div3=6\). In exams identify (a) and (r) separately.
Step 2
Why this answer is correct
The correct answer is A. (a=3,r=6). The first term is (3) and the ratio is \(18\div3=6\). In exams identify (a) and (r) separately.
Step 3
Exam Tip
पहला पद (3) है और अनुपात \(18\div3=6\) है। परीक्षा में (a) और (r) अलग-अलग पहचानें।
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यदि किसी गुणोत्तर श्रेणी में (a=10) और (r=2) है तो पाँचवाँ पद क्या होगा?
If a geometric progression has (a=10) and (r=2) what is the fifth term?
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A (80)
B (120)
C (160)
D (320)
Explanation opens after your attempt
Step 1
Concept
\(a_5=10\cdot2^4=160\). In exams use \(r^4\) for the fifth term.
Step 2
Why this answer is correct
The correct answer is C. (160). \(a_5=10\cdot2^4=160\). In exams use \(r^4\) for the fifth term.
Step 3
Exam Tip
\(a_5=10\cdot2^4=160\) है। परीक्षा में पाँचवें पद के लिए \(r^4\) लगाएँ।
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अनुक्रम \(6,18,54,162,\ldots\) में (486) कौन-सा पद है?
In the sequence \(6,18,54,162,\ldots\) which term is (486)?
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A चौथा पद / (4)th term
B पाँचवाँ पद / (5)th term
C छठा पद / (6)th term
D सातवाँ पद / (7)th term
Explanation opens after your attempt
Correct Answer
B. पाँचवाँ पद / (5)th term
Step 1
Concept
The terms are (6,18,54,162,486) so (486) is the fifth term. In exams count the first term too.
Step 2
Why this answer is correct
The correct answer is B. पाँचवाँ पद / (5)th term. The terms are (6,18,54,162,486) so (486) is the fifth term. In exams count the first term too.
Step 3
Exam Tip
पद (6,18,54,162,486) हैं इसलिए (486) पाँचवाँ पद है। परीक्षा में पहला पद भी गिनें।
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यदि गुणोत्तर श्रेणी में \(a_1=12\) और \(a_2=48\) है तो सामान्य अनुपात क्या होगा?
If a geometric progression has \(a_1=12\) and \(a_2=48\) what is the common ratio?
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(a_2\div a_1=48\div12=4\). In exams take the ratio of two consecutive terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The common ratio is \(a_2\div a_1=48\div12=4\). In exams take the ratio of two consecutive terms.
Step 3
Exam Tip
सामान्य अनुपात \(a_2\div a_1=48\div12=4\) है। परीक्षा में दो लगातार पदों का अनुपात लें।
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गुणोत्तर श्रेणी \(13,26,52,104,\ldots\) का अगला पद क्या है?
What is the next term of the geometric progression \(13,26,52,104,\ldots\)?
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A (156)
B (182)
C (208)
D (260)
Explanation opens after your attempt
Step 1
Concept
The common ratio is (2) so the next term is \(104\times2=208\). In exams multiply the last known term by the ratio.
Step 2
Why this answer is correct
The correct answer is C. (208). The common ratio is (2) so the next term is \(104\times2=208\). In exams multiply the last known term by the ratio.
Step 3
Exam Tip
सामान्य अनुपात (2) है इसलिए अगला पद \(104\times2=208\) है। परीक्षा में अंतिम ज्ञात पद में अनुपात से गुणा करें।
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गुणोत्तर श्रेणी \(240,120,60,30,\ldots\) में पाँचवाँ पद क्या है?
What is the fifth term in the geometric progression \(240,120,60,30,\ldots\)?
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A (10)
B (15)
C (20)
D (25)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(\frac{1}{2}\) so the fifth term is \(30\times\frac{1}{2}=15\). In exams apply fractional ratios carefully.
Step 2
Why this answer is correct
The correct answer is B. (15). The common ratio is \(\frac{1}{2}\) so the fifth term is \(30\times\frac{1}{2}=15\). In exams apply fractional ratios carefully.
Step 3
Exam Tip
सामान्य अनुपात \(\frac{1}{2}\) है इसलिए पाँचवाँ पद \(30\times\frac{1}{2}=15\) है। परीक्षा में भिन्न अनुपात ध्यान से लगाएँ।
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यदि गुणोत्तर श्रेणी \(z,,5z,,25z,\ldots\) है तो सामान्य अनुपात क्या है?
If \(z,,5z,,25z,\ldots\) is a geometric progression what is the common ratio?
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A (z)
B (5)
C (25)
D (125)
Explanation opens after your attempt
Step 1
Concept
The ratio of the second term to the first term is \(5z\div z=5\). In exams divide even with algebraic terms.
Step 2
Why this answer is correct
The correct answer is B. (5). The ratio of the second term to the first term is \(5z\div z=5\). In exams divide even with algebraic terms.
Step 3
Exam Tip
दूसरे पद और पहले पद का अनुपात \(5z\div z=5\) है। परीक्षा में बीजीय पदों में भी भाग करें।
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गुणोत्तर श्रेणी \(11,11,11,11,\ldots\) में सामान्य अनुपात क्या है?
What is the common ratio in the geometric progression \(11,11,11,11,\ldots\)?
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A (0)
B (1)
C (11)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Consecutive terms are equal so the ratio is \(11\div11=1\). In exams a non-zero constant sequence can also be a geometric progression.
Step 2
Why this answer is correct
The correct answer is B. (1). Consecutive terms are equal so the ratio is \(11\div11=1\). In exams a non-zero constant sequence can also be a geometric progression.
Step 3
Exam Tip
लगातार पद समान हैं इसलिए अनुपात \(11\div11=1\) है। परीक्षा में स्थिर शून्येतर श्रेणी भी गुणोत्तर श्रेणी हो सकती है।
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यदि (a=17) और (r=1) है तो पहले तीन पद क्या होंगे?
If (a=17) and (r=1) what are the first three terms?
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A (17,1,17)
B (1,17,289)
C (17,17,17)
D (17,34,68)
Explanation opens after your attempt
Correct Answer
C. (17,17,17)
Step 1
Concept
When the common ratio is (1) all terms remain (17). In exams (r=1) means a constant geometric progression.
Step 2
Why this answer is correct
The correct answer is C. (17,17,17). When the common ratio is (1) all terms remain (17). In exams (r=1) means a constant geometric progression.
Step 3
Exam Tip
सामान्य अनुपात (1) होने पर सभी पद (17) रहेंगे। परीक्षा में (r=1) का मतलब स्थिर गुणोत्तर श्रेणी है।
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गुणोत्तर श्रेणी \(4,\Box,100,500,\ldots\) में रिक्त पद क्या होगा?
What is the missing term in the geometric progression \(4,\Box,100,500,\ldots\)?
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A (10)
B (20)
C (25)
D (50)
Explanation opens after your attempt
Step 1
Concept
The ratio of (100) and (500) is (5) so the missing term is \(100\div5=20\). In exams apply the common ratio backward too.
Step 2
Why this answer is correct
The correct answer is B. (20). The ratio of (100) and (500) is (5) so the missing term is \(100\div5=20\). In exams apply the common ratio backward too.
Step 3
Exam Tip
(100) और (500) का अनुपात (5) है इसलिए रिक्त पद \(100\div5=20\) है। परीक्षा में पीछे की ओर भी सामान्य अनुपात लगाएँ।
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यदि \(a_n=9\cdot3^{n-1}\) है तो इस गुणोत्तर श्रेणी का सामान्य अनुपात क्या है?
If \(a_n=9\cdot3^{n-1}\) what is the common ratio of this geometric progression?
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
In the formula \(a_n=9\cdot3^{n-1}\) the common ratio is (3). In exams identify (r) in \(ar^{n-1}\).
Step 2
Why this answer is correct
The correct answer is A. (3). In the formula \(a_n=9\cdot3^{n-1}\) the common ratio is (3). In exams identify (r) in \(ar^{n-1}\).
Step 3
Exam Tip
सूत्र \(a_n=9\cdot3^{n-1}\) में (3) ही सामान्य अनुपात है। परीक्षा में \(ar^{n-1}\) में (r) पहचानें।
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गुणोत्तर श्रेणी \(16,64,256,1024,\ldots\) का \(a_5\) क्या है?
What is \(a_5\) of the geometric progression \(16,64,256,1024,\ldots\)?
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A (2048)
B (3072)
C (4096)
D (8192)
Explanation opens after your attempt
Step 1
Concept
(r=4) so \(a_5=1024\times4=4096\). In exams multiply by the ratio (n-1) times.
Step 2
Why this answer is correct
The correct answer is C. (4096). (r=4) so \(a_5=1024\times4=4096\). In exams multiply by the ratio (n-1) times.
Step 3
Exam Tip
(r=4) है इसलिए \(a_5=1024\times4=4096\) है। परीक्षा में (n-1) बार अनुपात से गुणा करें।
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यदि गुणोत्तर श्रेणी में \(a_1=7\) और (r=5) है तो \(a_3\) क्या होगा?
If a geometric progression has \(a_1=7\) and (r=5) what is \(a_3\)?
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A (105)
B (125)
C (175)
D (245)
Explanation opens after your attempt
Step 1
Concept
\(a_3=7\cdot5^2=175\). In exams use \(r^2\) for the third term.
Step 2
Why this answer is correct
The correct answer is C. (175). \(a_3=7\cdot5^2=175\). In exams use \(r^2\) for the third term.
Step 3
Exam Tip
\(a_3=7\cdot5^2=175\) है। परीक्षा में तीसरे पद के लिए \(r^2\) लगाएँ।
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गुणोत्तर श्रेणी \(3,6,12,24,\ldots\) का दसवाँ पद क्या है?
What is the tenth term of the geometric progression \(3,6,12,24,\ldots\)?
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A (768)
B (1536)
C (3072)
D (384)
Explanation opens after your attempt
Step 1
Concept
This is of the form \(3\cdot2^{n-1}\) so the tenth term is \(3\cdot2^9=1536\). In exams identify powers to solve quickly.
Step 2
Why this answer is correct
The correct answer is B. (1536). This is of the form \(3\cdot2^{n-1}\) so the tenth term is \(3\cdot2^9=1536\). In exams identify powers to solve quickly.
Step 3
Exam Tip
यह \(3\cdot2^{n-1}\) के रूप में है इसलिए दसवाँ पद \(3\cdot2^9=1536\) है। परीक्षा में घात पहचानकर जल्दी हल करें।
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यदि \(a_n=2\cdot5^{n-1}\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=2\cdot5^{n-1}\) what is the value of \(a_4\)?
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A (125)
B (200)
C (250)
D (500)
Explanation opens after your attempt
Step 1
Concept
\(a_4=2\cdot5^3=250\). In exams calculate the power carefully.
Step 2
Why this answer is correct
The correct answer is C. (250). \(a_4=2\cdot5^3=250\). In exams calculate the power carefully.
Step 3
Exam Tip
\(a_4=2\cdot5^3=250\) है। परीक्षा में घात का मान ध्यान से निकालें।
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गुणोत्तर श्रेणी \(60,30,15,\frac{15}{2},\ldots\) का सामान्य पद क्या है?
What is the general term of the geometric progression \(60,30,15,\frac{15}{2},\ldots\)?
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A \(a_n=60\cdot\left(\frac{1}{2}\right)^{n-1}\)
B \(a_n=60\cdot2^{n-1}\)
C \(a_n=60-n\)
D \(a_n=30n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=60\cdot\left(\frac{1}{2}\right)^{n-1}\)
Step 1
Concept
The first term is (60) and the ratio is \(\frac{1}{2}\). In exams put the correct fractional ratio in \(ar^{n-1}\).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=60\cdot\left(\frac{1}{2}\right)^{n-1}\). The first term is (60) and the ratio is \(\frac{1}{2}\). In exams put the correct fractional ratio in \(ar^{n-1}\).
Step 3
Exam Tip
पहला पद (60) और अनुपात \(\frac{1}{2}\) है। परीक्षा में \(ar^{n-1}\) में सही भिन्न अनुपात रखें।
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यदि गुणोत्तर श्रेणी (10,,x,,90) है तो (x) का धनात्मक मान क्या होगा?
If (10,,x,,90) is a geometric progression what is the positive value of (x)?
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A (20)
B (30)
C (40)
D (45)
Explanation opens after your attempt
Step 1
Concept
The square of the middle term is \(10\times90=900\) so the positive (x=30). In exams for three GP terms the square of the middle term equals the product of the outer terms.
Step 2
Why this answer is correct
The correct answer is B. (30). The square of the middle term is \(10\times90=900\) so the positive (x=30). In exams for three GP terms the square of the middle term equals the product of the outer terms.
Step 3
Exam Tip
मध्य पद का वर्ग \(10\times90=900\) है इसलिए धनात्मक (x=30) है। परीक्षा में तीन पदों वाली गुणोत्तर श्रेणी में मध्य पद का वर्ग बाहरी पदों के गुणनफल के बराबर होता है।
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गुणोत्तर श्रेणी \(18,54,162,486,\ldots\) में पाँचवाँ पद क्या होगा?
What will be the fifth term in the geometric progression \(18,54,162,486,\ldots\)?
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A (972)
B (1215)
C (1458)
D (1944)
Explanation opens after your attempt
Step 1
Concept
The common ratio is (3) so the fifth term is \(486\times3=1458\). In exams multiply the last known term by the ratio.
Step 2
Why this answer is correct
The correct answer is C. (1458). The common ratio is (3) so the fifth term is \(486\times3=1458\). In exams multiply the last known term by the ratio.
Step 3
Exam Tip
सामान्य अनुपात (3) है इसलिए पाँचवाँ पद \(486\times3=1458\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें।
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किस गुणोत्तर श्रेणी का पहला पद (8) और सामान्य अनुपात (3) है?
Which geometric progression has first term (8) and common ratio (3)?
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A \(8,24,72,216,\ldots\)
B \(3,9,27,81,\ldots\)
C \(8,11,14,17,\ldots\)
D \(24,72,216,648,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(8,24,72,216,\ldots\)
Step 1
Concept
The first term is (8) and each term is multiplied by (3). In exams match both the first term and the ratio.
Step 2
Why this answer is correct
The correct answer is A. \(8,24,72,216,\ldots\). The first term is (8) and each term is multiplied by (3). In exams match both the first term and the ratio.
Step 3
Exam Tip
पहला पद (8) है और हर बार (3) से गुणा हो रहा है। परीक्षा में पहला पद और अनुपात दोनों मिलाएँ।
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यदि (a=12) और (r=2) है तो गुणोत्तर श्रेणी का छठा पद क्या होगा?
If (a=12) and (r=2) what will be the sixth term of the geometric progression?
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A (192)
B (288)
C (384)
D (512)
Explanation opens after your attempt
Step 1
Concept
The sixth term is \(ar^5=12\cdot2^5=384\). In exams use \(r^{n-1}\) for the (n)th term.
Step 2
Why this answer is correct
The correct answer is C. (384). The sixth term is \(ar^5=12\cdot2^5=384\). In exams use \(r^{n-1}\) for the (n)th term.
Step 3
Exam Tip
छठा पद \(ar^5=12\cdot2^5=384\) है। परीक्षा में (n)वें पद के लिए \(r^{n-1}\) लगाएँ।
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यदि गुणोत्तर श्रेणी में \(a_2=15\) और (r=3) है तो \(a_3\) क्या होगा?
If a geometric progression has \(a_2=15\) and (r=3) what is \(a_3\)?
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A (30)
B (45)
C (60)
D (75)
Explanation opens after your attempt
Step 1
Concept
The third term is \(a_3=a_2\times r=15\times3=45\). In exams multiply the previous term by the ratio to get the next term.
Step 2
Why this answer is correct
The correct answer is B. (45). The third term is \(a_3=a_2\times r=15\times3=45\). In exams multiply the previous term by the ratio to get the next term.
Step 3
Exam Tip
तीसरा पद \(a_3=a_2\times r=15\times3=45\) है। परीक्षा में अगले पद के लिए पिछले पद को अनुपात से गुणा करें।
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