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A sequence is given by log7 2, log7 4, log7 16, log7 256, ........... The common ratio of this geometric progression is
- a)log7 2
- b)2
- c)2 log7 2
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A sequence is given by log7 2, log7 4, log7 16, log7 256, ........... ...
Given sequence can be written as follows.
log7 2, log7 22, log7 24, log7 28, ……….
It can be further written as
log7 2, 2 log7 2, 4 log7 2, 8 log7 2, ………. [log mn = n log m]
By dividing 2nd term by 1st term, we get common ratio, r =
= 2
log7 2, log7 22, log7 24, log7 28, ……….
It can be further written as
log7 2, 2 log7 2, 4 log7 2, 8 log7 2, ………. [log mn = n log m]
By dividing 2nd term by 1st term, we get common ratio, r =
= 2Free Test
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Community Answer
A sequence is given by log7 2, log7 4, log7 16, log7 256, ........... ...
Given sequence:
The given sequence is log7 2, log7 4, log7 16, log7 256, ........
Observation:
From the given sequence, we can see that each term is obtained by taking the logarithm of the previous term to the base 7 and then multiplying it by 2.
Let's find the common ratio:
To find the common ratio, we divide each term by its previous term.
log7 4 / log7 2 = log2 4 / log2 2 = 2 / 1 = 2
log7 16 / log7 4 = log2 16 / log2 4 = 4 / 2 = 2
log7 256 / log7 16 = log2 256 / log2 16 = 8 / 4 = 2
We can see that the common ratio is 2.
Conclusion:
Therefore, the common ratio of the given geometric progression is 2. Hence, the correct answer is option B.
The given sequence is log7 2, log7 4, log7 16, log7 256, ........
Observation:
From the given sequence, we can see that each term is obtained by taking the logarithm of the previous term to the base 7 and then multiplying it by 2.
Let's find the common ratio:
To find the common ratio, we divide each term by its previous term.
log7 4 / log7 2 = log2 4 / log2 2 = 2 / 1 = 2
log7 16 / log7 4 = log2 16 / log2 4 = 4 / 2 = 2
log7 256 / log7 16 = log2 256 / log2 16 = 8 / 4 = 2
We can see that the common ratio is 2.
Conclusion:
Therefore, the common ratio of the given geometric progression is 2. Hence, the correct answer is option B.
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