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In the given Geometric progression find the number of terms. 32, 256, 2048, 16384,.........,250.
- a)None of the mentioned
- b)11
- c)13
- d)15
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In the given Geometric progression find the number of terms. 32, 256, ...
nth term = first term(ration – 1)., 250 = 25(23(n-1)), n = 15. This implies the 16th term
Most Upvoted Answer
In the given Geometric progression find the number of terms. 32, 256, ...
Given, the geometric progression is 32, 256, 2048, 16384,.........,250.
To find the number of terms in the given geometric progression, we need to use the formula for the nth term of a geometric progression:
an = a1 * r^(n-1)
where,
an = nth term
a1 = first term
r = common ratio
n = number of terms
We can see that the common ratio is 256/32 = 8.
So, the nth term can be written as:
an = 32 * 8^(n-1)
Now, we need to find the value of n for which an = 250.
So, we have:
250 = 32 * 8^(n-1)
Dividing both sides by 32, we get:
8^(n-1) = 250/32
8^(n-1) = 7.8125
Taking logarithm on both sides, we get:
(n-1) log 8 = log 7.8125
n-1 = log 7.8125 / log 8
n-1 = 1.0631
Adding 1 on both sides, we get:
n = 2.0631
Since n is not a whole number, it means that there are no such number of terms that exist for the given geometric progression.
Hence, the correct answer is option A, i.e. None of the mentioned.
To find the number of terms in the given geometric progression, we need to use the formula for the nth term of a geometric progression:
an = a1 * r^(n-1)
where,
an = nth term
a1 = first term
r = common ratio
n = number of terms
We can see that the common ratio is 256/32 = 8.
So, the nth term can be written as:
an = 32 * 8^(n-1)
Now, we need to find the value of n for which an = 250.
So, we have:
250 = 32 * 8^(n-1)
Dividing both sides by 32, we get:
8^(n-1) = 250/32
8^(n-1) = 7.8125
Taking logarithm on both sides, we get:
(n-1) log 8 = log 7.8125
n-1 = log 7.8125 / log 8
n-1 = 1.0631
Adding 1 on both sides, we get:
n = 2.0631
Since n is not a whole number, it means that there are no such number of terms that exist for the given geometric progression.
Hence, the correct answer is option A, i.e. None of the mentioned.
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