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 .
Let the sum of n terms of the G.P. be 315.
It is known that,
Sn=a(rn−1)r−1
It
is given that the first term a
is 5 and common ratio r is 2.
∴315=5(2n−1)2−1⇒2n−1=63⇒2n=64=26⇒n=6
∴ Last term of the G.P.:
6th term =ar6−1=(5)(2)5=(5)(32)=160.
Thus, the last term of the G.P.
is 160.