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The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. is
- a)-1
- b)2
- c)4
- d)-4
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common...
The nth tan of a G.P is (tn) = arn - 1
t6 = a.r5 = 32
t8 = a.r7 = 128
∴ =
or =
or r2 = (2)2
or r = 2
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t6 = a.r5 = 32
t8 = a.r7 = 128
∴ =
or =
or r2 = (2)2
or r = 2
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The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common...
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The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common...
The formula to find the nth term of a geometric progression (G.P.) is given by:
an = a * r^(n-1)
Where:
an = nth term of the G.P.
a = first term of the G.P.
r = common ratio of the G.P.
n = term number
Given that the 6th term (a6) is 32, we can substitute the values into the formula:
32 = a * r^(6-1)
32 = a * r^5
Similarly, the 8th term (a8) is given as 128:
128 = a * r^(8-1)
128 = a * r^7
To find the common ratio (r), we can divide the equation for the 8th term by the equation for the 6th term:
(128 / 32) = (a * r^7) / (a * r^5)
4 = r^2
√4 = r
r = 2 or -2
Both 2 and -2 are valid solutions for the common ratio. However, we can determine which one is correct by substituting the values back into the equations.
For r = 2:
32 = a * 2^5
32 = a * 32
a = 1
For r = -2:
32 = a * (-2)^5
32 = a * (-32)
a = -1
Since the first term (a) is not specified in the question, it can have multiple values. However, the common ratio (r) can only be either 2 or -2.
Therefore, the correct answer is option 'B', r = 2.
an = a * r^(n-1)
Where:
an = nth term of the G.P.
a = first term of the G.P.
r = common ratio of the G.P.
n = term number
Given that the 6th term (a6) is 32, we can substitute the values into the formula:
32 = a * r^(6-1)
32 = a * r^5
Similarly, the 8th term (a8) is given as 128:
128 = a * r^(8-1)
128 = a * r^7
To find the common ratio (r), we can divide the equation for the 8th term by the equation for the 6th term:
(128 / 32) = (a * r^7) / (a * r^5)
4 = r^2
√4 = r
r = 2 or -2
Both 2 and -2 are valid solutions for the common ratio. However, we can determine which one is correct by substituting the values back into the equations.
For r = 2:
32 = a * 2^5
32 = a * 32
a = 1
For r = -2:
32 = a * (-2)^5
32 = a * (-32)
a = -1
Since the first term (a) is not specified in the question, it can have multiple values. However, the common ratio (r) can only be either 2 or -2.
Therefore, the correct answer is option 'B', r = 2.
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The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer?
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The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer?.
The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 6th term of a G.P. is 32 and its 8th term is 128 ; then the common ratio of the G.P. isa) -1 b) 2 c) 4 d) -4 Correct answer is option 'B'. Can you explain this answer?.
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