गुणोत्तर श्रेढ़ी में \(a_1=10\) और \(a_4=270\) है। धनात्मक (r) क्या होगा?
In a geometric progression, \(a_1=10\) and \(a_4=270\). What will be the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1r^3\), so \(270=10r^3\) and \(r^3=27\), hence (r=3). Use the position gap as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_4=a_1r^3\), so \(270=10r^3\) and \(r^3=27\), hence (r=3). Use the position gap as the exponent.
Step 3
Exam Tip
\(a_4=a_1r^3\), इसलिए \(270=10r^3\) और \(r^3=27\), अतः (r=3)। पदों की दूरी को घात बनाएं।
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यदि \(a_4=54\) और \(a_8=4374\) है, तथा (r) धनात्मक है, तो (r) क्या है?
If \(a_4=54\) and \(a_8=4374\), and (r) is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_8=a_4r^4\), so \(4374=54r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_8=a_4r^4\), so \(4374=54r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 3
Exam Tip
\(a_8=a_4r^4\), इसलिए \(4374=54r^4\) और \(r^4=81\), अतः (r=3)। चार पदों की दूरी पर \(r^4\) लगता है।
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यदि \(a_1=7\) और \(a_5=1792\) है, तो धनात्मक सार्व अनुपात क्या होगा?
If \(a_1=7\) and \(a_5=1792\), what will be the positive common ratio?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_1r^4\), so \(1792=7r^4\) and \(r^4=256\), hence (r=4). When positive ratio is asked, take the positive root.
Step 2
Why this answer is correct
The correct answer is C. (4). \(a_5=a_1r^4\), so \(1792=7r^4\) and \(r^4=256\), hence (r=4). When positive ratio is asked, take the positive root.
Step 3
Exam Tip
\(a_5=a_1r^4\), इसलिए \(1792=7r^4\) और \(r^4=256\), अतः (r=4)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
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गुणोत्तर श्रेढ़ी में \(a_3=18\) और \(a_6=486\) है। धनात्मक सार्व अनुपात (r) क्या होगा?
In a geometric progression, \(a_3=18\) and \(a_6=486\). What is the positive common ratio (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_3r^3\), so \(486=18r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_6=a_3r^3\), so \(486=18r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 3
Exam Tip
\(a_6=a_3r^3\), इसलिए \(486=18r^3\) और (r=3)। पदों की दूरी को घात बनाएं।
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गुणोत्तर श्रेढ़ी \(a,ar,ar^2,\ldots\) में \(a_1=9\) और \(a_4=72\) है। धनात्मक (r) क्या होगा?
In the geometric progression \(a,ar,ar^2,\ldots\), \(a_1=9\) and \(a_4=72\). What will be the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1r^3\), so \(72=9r^3\) and \(r^3=8\), hence (r=2). Use the position gap as the exponent.
Step 2
Why this answer is correct
The correct answer is A. (2). \(a_4=a_1r^3\), so \(72=9r^3\) and \(r^3=8\), hence (r=2). Use the position gap as the exponent.
Step 3
Exam Tip
\(a_4=a_1r^3\), इसलिए \(72=9r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी को घात बनाएं।
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यदि \(a_3=45\) और \(a_7=3645\) है, तथा (r) धनात्मक है, तो (r) क्या है?
If \(a_3=45\) and \(a_7=3645\), and (r) is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_7=a_3r^4\), so \(3645=45r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_7=a_3r^4\), so \(3645=45r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 3
Exam Tip
\(a_7=a_3r^4\), इसलिए \(3645=45r^4\) और \(r^4=81\), अतः (r=3)। चार पदों की दूरी पर \(r^4\) लगता है।
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यदि \(a_1=3\) और \(a_5=243\) है, तो धनात्मक सार्व अनुपात क्या होगा?
If \(a_1=3\) and \(a_5=243\), what will be the positive common ratio?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_1r^4\), so \(243=3r^4\) and \(r^4=81\), hence (r=3). When positive ratio is asked, take the positive root.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=a_1r^4\), so \(243=3r^4\) and \(r^4=81\), hence (r=3). When positive ratio is asked, take the positive root.
Step 3
Exam Tip
\(a_5=a_1r^4\), इसलिए \(243=3r^4\) और \(r^4=81\), अतः (r=3)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
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गुणोत्तर श्रेढ़ी में \(a_4=54\) और \(a_7=1458\) है। धनात्मक सार्व अनुपात (r) क्या होगा?
In a geometric progression, \(a_4=54\) and \(a_7=1458\). What will be the positive common ratio (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_7=a_4r^3\), so \(1458=54r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_7=a_4r^3\), so \(1458=54r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 3
Exam Tip
\(a_7=a_4r^3\), इसलिए \(1458=54r^3\) और (r=3)। पदों की दूरी को घात बनाएं।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=6\) और \(a_3=150\) है, तो धनात्मक (r) क्या होगा?
If a geometric progression has \(a_1=6\) and \(a_3=150\), what is the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_3=a_1r^2\), so \(150=6r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 2
Why this answer is correct
The correct answer is C. (5). \(a_3=a_1r^2\), so \(150=6r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 3
Exam Tip
\(a_3=a_1r^2\), इसलिए \(150=6r^2\) और \(r^2=25\), अतः धनात्मक (r=5)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
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यदि \(a_2=40\) और \(a_5=320\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If \(a_2=40\) and \(a_5=320\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(320=40r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Step 2
Why this answer is correct
The correct answer is A. (2). \(a_5=a_2r^3\), so \(320=40r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(320=40r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी घात तय करती है।
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किस अनुक्रम का सार्व अनुपात (6) है?
Which sequence has common ratio (6)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(6,12,18,24,\ldots\)
B \(2,12,72,432,\ldots\)
C \(3,9,27,81,\ldots\)
D \(216,36,6,1,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(2,12,72,432,\ldots\)
Step 1
Concept
In \(2,12,72,432,\ldots\), each term is multiplied by (6). For the ratio divide the next term by the previous term.
Step 2
Why this answer is correct
The correct answer is B. \(2,12,72,432,\ldots\). In \(2,12,72,432,\ldots\), each term is multiplied by (6). For the ratio divide the next term by the previous term.
Step 3
Exam Tip
\(2,12,72,432,\ldots\) में हर बार (6) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें।
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यदि \(a_2=16\) और \(a_5=1024\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If \(a_2=16\) and \(a_5=1024\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(1024=16r^3\) and \(r^3=64\), hence (r=4). The gap between positions decides the exponent.
Step 2
Why this answer is correct
The correct answer is C. (4). \(a_5=a_2r^3\), so \(1024=16r^3\) and \(r^3=64\), hence (r=4). The gap between positions decides the exponent.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(1024=16r^3\) और \(r^3=64\), अतः (r=4)। पदों की दूरी घात तय करती है।
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किस विकल्प में सार्व अनुपात \(\frac{1}{3}\) है?
Which option has common ratio \(\frac{1}{3}\)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(3,9,27,81,\ldots\)
B \(81,27,9,3,\ldots\)
C \(1,3,9,27,\ldots\)
D \(27,9,6,2,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(81,27,9,3,\ldots\)
Step 1
Concept
In \(81,27,9,3,\ldots\), \(\frac{27}{81}=\frac{1}{3}\). Divide consecutive terms to find the ratio.
Step 2
Why this answer is correct
The correct answer is B. \(81,27,9,3,\ldots\). In \(81,27,9,3,\ldots\), \(\frac{27}{81}=\frac{1}{3}\). Divide consecutive terms to find the ratio.
Step 3
Exam Tip
\(81,27,9,3,\ldots\) में \(\frac{27}{81}=\frac{1}{3}\) है। अनुपात के लिए लगातार पदों को भाग दें।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=3\) और \(a_4=81\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If a geometric progression has \(a_1=3\) and \(a_4=81\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1r^3\), so \(81=3r^3\) and \(r^3=27\), hence (r=3). The position gap decides the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_4=a_1r^3\), so \(81=3r^3\) and \(r^3=27\), hence (r=3). The position gap decides the exponent.
Step 3
Exam Tip
\(a_4=a_1r^3\), इसलिए \(81=3r^3\) और \(r^3=27\), अतः (r=3)। पद-संख्या का अंतर घात तय करता है।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=3\) और \(a_3=75\) है, तो धनात्मक (r) क्या होगा?
If a geometric progression has \(a_1=3\) and \(a_3=75\), what is the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_3=a_1r^2\), so \(75=3r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 2
Why this answer is correct
The correct answer is C. (5). \(a_3=a_1r^2\), so \(75=3r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 3
Exam Tip
\(a_3=a_1r^2\), इसलिए \(75=3r^2\) और \(r^2=25\), अतः धनात्मक (r=5)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
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यदि \(a_2=30\) और \(a_5=810\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If \(a_2=30\) and \(a_5=810\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(810=30r^3\) and \(r^3=27\), hence (r=3). The gap between positions decides the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=a_2r^3\), so \(810=30r^3\) and \(r^3=27\), hence (r=3). The gap between positions decides the exponent.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(810=30r^3\) और \(r^3=27\), अतः (r=3)। पदों की दूरी घात तय करती है।
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किस अनुक्रम का सार्व अनुपात (4) है?
Which sequence has common ratio (4)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(4,8,12,16,\ldots\)
B \(3,12,48,192,\ldots\)
C \(2,6,18,54,\ldots\)
D \(64,16,4,1,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(3,12,48,192,\ldots\)
Step 1
Concept
In \(3,12,48,192,\ldots\), each term is multiplied by (4). For the ratio divide the next term by the previous term.
Step 2
Why this answer is correct
The correct answer is B. \(3,12,48,192,\ldots\). In \(3,12,48,192,\ldots\), each term is multiplied by (4). For the ratio divide the next term by the previous term.
Step 3
Exam Tip
\(3,12,48,192,\ldots\) में हर बार (4) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें।
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यदि किसी गुणोत्तर श्रेढ़ी में \(a_2=12\) और \(a_5=324\) है, तथा अनुपात धनात्मक है, तो (r) क्या होगा?
If a geometric progression has \(a_2=12\) and \(a_5=324\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(324=12r^3\) and \(r^3=27\), hence (r=3). The gap between positions decides the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=a_2r^3\), so \(324=12r^3\) and \(r^3=27\), hence (r=3). The gap between positions decides the exponent.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(324=12r^3\) और \(r^3=27\), अतः (r=3)। पदों की दूरी घात तय करती है।
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किस विकल्प में सार्व अनुपात \(\frac{1}{5}\) है?
Which option has common ratio \(\frac{1}{5}\)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(5,25,125,625,\ldots\)
B \(1,5,25,125,\ldots\)
C \(100,20,4,\frac{4}{5},\ldots\)
D \(25,10,4,\frac{8}{5},\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(100,20,4,\frac{4}{5},\ldots\)
Step 1
Concept
In \(100,20,4,\frac{4}{5},\ldots\), \(\frac{20}{100}=\frac{1}{5}\). Divide consecutive terms to find the ratio.
Step 2
Why this answer is correct
The correct answer is C. \(100,20,4,\frac{4}{5},\ldots\). In \(100,20,4,\frac{4}{5},\ldots\), \(\frac{20}{100}=\frac{1}{5}\). Divide consecutive terms to find the ratio.
Step 3
Exam Tip
\(100,20,4,\frac{4}{5},\ldots\) में \(\frac{20}{100}=\frac{1}{5}\) है। अनुपात के लिए लगातार पदों को भाग दें।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=2\) और \(a_5=162\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If a geometric progression has \(a_1=2\) and \(a_5=162\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_1r^4\), so \(162=2r^4\) and \(r^4=81\), hence (r=3). The position gap decides the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=a_1r^4\), so \(162=2r^4\) and \(r^4=81\), hence (r=3). The position gap decides the exponent.
Step 3
Exam Tip
\(a_5=a_1r^4\), इसलिए \(162=2r^4\) और \(r^4=81\), अतः (r=3)। पद-संख्या का अंतर घात तय करता है।
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अनुक्रम \(5,15,45,135,\ldots\) में सार्व अनुपात क्या है?
What is the common ratio in the sequence \(5,15,45,135,\ldots\)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (4)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(\frac{15}{5}=3\). In a geometric progression divide the next term by the previous term.
Step 2
Why this answer is correct
The correct answer is C. (3). The common ratio is \(\frac{15}{5}=3\). In a geometric progression divide the next term by the previous term.
Step 3
Exam Tip
सार्व अनुपात \(\frac{15}{5}=3\) है। गुणोत्तर श्रेढ़ी में अगला पद पिछले पद से भाग दें।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=2\) और \(a_3=50\) है, तो धनात्मक (r) क्या होगा?
If a geometric progression has \(a_1=2\) and \(a_3=50\), what is the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_3=a_1r^2\), so \(50=2r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 2
Why this answer is correct
The correct answer is C. (5). \(a_3=a_1r^2\), so \(50=2r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
Step 3
Exam Tip
\(a_3=a_1r^2\), इसलिए \(50=2r^2\) और \(r^2=25\), अतः धनात्मक (r=5)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
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यदि \(a_2=24\) और \(a_5=192\) है, तथा अनुपात धनात्मक है, तो (r) क्या है?
If \(a_2=24\) and \(a_5=192\), and the ratio is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(192=24r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Step 2
Why this answer is correct
The correct answer is A. (2). \(a_5=a_2r^3\), so \(192=24r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(192=24r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी घात तय करती है।
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किस अनुक्रम का सार्व अनुपात (5) है?
Which sequence has common ratio (5)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(5,10,15,20,\ldots\)
B \(2,10,50,250,\ldots\)
C \(1,5,25,100,\ldots\)
D \(25,5,1,\frac{1}{5},\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(2,10,50,250,\ldots\)
Step 1
Concept
In \(2,10,50,250,\ldots\), each term is multiplied by (5). For the ratio divide the next term by the previous term.
Step 2
Why this answer is correct
The correct answer is B. \(2,10,50,250,\ldots\). In \(2,10,50,250,\ldots\), each term is multiplied by (5). For the ratio divide the next term by the previous term.
Step 3
Exam Tip
\(2,10,50,250,\ldots\) में हर बार (5) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें।
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यदि किसी गुणोत्तर श्रेढ़ी में \(a_2=18\) और \(a_4=162\) है, तो (r) क्या होगा?
If a geometric progression has \(a_2=18\) and \(a_4=162\), what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_2r^2\), so \(162=18r^2\) and \(r^2=9\), giving positive ratio (r=3). Use the gap between terms as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_4=a_2r^2\), so \(162=18r^2\) and \(r^2=9\), giving positive ratio (r=3). Use the gap between terms as the exponent.
Step 3
Exam Tip
\(a_4=a_2r^2\), इसलिए \(162=18r^2\) और \(r^2=9\), धनात्मक अनुपात (r=3) है। पदों के बीच दूरी को घात बनाएं।
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किस विकल्प में सार्व अनुपात \(\frac{1}{4}\) है?
Which option has common ratio \(\frac{1}{4}\)?
#sequences
#progressions
#geometric-progression
#common-ratio
A \(4,8,16,32,\ldots\)
B \(64,16,4,1,\ldots\)
C \(1,4,16,64,\ldots\)
D \(8,4,2,1,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(64,16,4,1,\ldots\)
Step 1
Concept
In \(64,16,4,1,\ldots\), \(\frac{16}{64}=\frac{1}{4}\). Divide consecutive terms to find the ratio.
Step 2
Why this answer is correct
The correct answer is B. \(64,16,4,1,\ldots\). In \(64,16,4,1,\ldots\), \(\frac{16}{64}=\frac{1}{4}\). Divide consecutive terms to find the ratio.
Step 3
Exam Tip
\(64,16,4,1,\ldots\) में \(\frac{16}{64}=\frac{1}{4}\) है। अनुपात के लिए लगातार पदों को भाग दें।
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यदि गुणोत्तर श्रेढ़ी में \(a_1=4\) और \(a_4=108\) है, तो सार्व अनुपात क्या है?
If a geometric progression has \(a_1=4\) and \(a_4=108\), what is the common ratio?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1r^3\), so \(108=4r^3\) and \(r^3=27\), hence (r=3). Use the position gap as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_4=a_1r^3\), so \(108=4r^3\) and \(r^3=27\), hence (r=3). Use the position gap as the exponent.
Step 3
Exam Tip
\(a_4=a_1r^3\), इसलिए \(108=4r^3\) और \(r^3=27\), अतः (r=3)। पद-संख्या के अंतर को घात बनाएं।
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अनुक्रम \(81,27,9,3,\ldots\) का सार्व अनुपात क्या है?
What is the common ratio of the sequence \(81,27,9,3,\ldots\)?
#sequences
#progressions
#geometric-progression
#common-ratio
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 common ratio is \(\frac{27}{81}=\frac{1}{3}\). In a decreasing geometric progression the ratio can be less than (1).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). The common ratio is \(\frac{27}{81}=\frac{1}{3}\). In a decreasing geometric progression the ratio can be less than (1).
Step 3
Exam Tip
सार्व अनुपात \(\frac{27}{81}=\frac{1}{3}\) है। घटती गुणोत्तर श्रेढ़ी में अनुपात (1) से छोटा हो सकता है।
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अनुक्रम \(3,6,12,24,\ldots\) में सार्व अनुपात क्या है?
What is the common ratio in the sequence \(3,6,12,24,\ldots\)?
#sequences
#progressions
#geometric-progression
#common-ratio
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The common ratio is \(\frac{6}{3}=2\). In a geometric progression divide the second term by the first term.
Step 2
Why this answer is correct
The correct answer is A. (2). The common ratio is \(\frac{6}{3}=2\). In a geometric progression divide the second term by the first term.
Step 3
Exam Tip
सार्व अनुपात \(\frac{6}{3}=2\) है। गुणोत्तर श्रेढ़ी में दूसरा पद पहले पद से भाग दें।
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