# The sum of some terms of G.P. is 316 whose first term and the common ratio are 6 and 2, respectively. Find the last term and the number of terms.

Given: Sum of n terms of the G.P. be 316.
a = 6, r = 2

To Find: n and an

Formula used: where Sn = Sum to n terms of G.P,
a = first term,
r = common ratio,
n = number of terms

It is given that the first term a is 6 and common ratio r is 2.

Applying the values in formula we get,     n = 6

nth term of G.P is given by -

an = a r n - 1

∴ Last term of the G.P = 6th term = ar6 - 1 = (6)(2) 5 = (6)(32) = 192

Thus, the last term of the G.P. is 192.

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