Maths-
General
Easy
Question
Fifth term of G.P is 2 The product of its first nine terms is
- 1024
- 256
- 512
- 356
Hint:
Given is only the fifth term of the G.P. and asked to find the product of 9 terms. We will consider the first term as a and the r be the common ratio of the whole G.P. then we can simply equate the fifth term as 
. Then remaining 9 terms will be multiplied such that their product will be in the form of
and we will try to adjust this in the form of fifth term. So let’s solve it!
The correct answer is: 512
Detailed Solution
Given that
term of a G.P. is 2
Let first term as a and the r be the common ratio of the whole G.P.
Then fifth term will be
But we are asked to find the product of 9 terms of the G.P.
So we can write the product as
So ,
Now we can write the terms with base a separately and those with r separately.
Now adding the powers of the bases separately,
But we have to write this in the form of power 4,
Now we will take the common power out,
Putting the value of fifth term in above bracket,
Thus, the product of its first nine terms is 512.
Here note that the fifth term is having fourth power of 2 and not fifth power. We need not to find all nine terms separately; only finding the product is enough because that product will then be written in the form of the term that is known. Terms in a G.P. are having a common ratio in between. That’s why the power of r is increasing as the terms are increasing.
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