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Question

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms .

Solution
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Let the sum of n terms of the G.P. be 315.
It is known that, Sn=a(rn1)r1
It is given that the first term a is 5 and common ratio r is 2.
315=5(2n1)212n1=632n=64=26n=6
Last term of the G.P.:
6th term =ar61=(5)(2)5=(5)(32)=160.
Thus, the last term of the G.P. is 160.

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