# The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

Given: The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128.

Let a, ar, ar2, ar3, ar4, ar5 be the terms of the G.P

Here a + ar +ar2 = 16 ( given that sum of first 3 terms is 16) -------–1

Also, ar3, ar4, ar5 = 128 ( given that sum of next 3 terms is 128)--------------–2

Divide eq –2 and eq –1

We get,

r3 = 8

r = 8

r = 2

Here a + ar + ar2 = 16

a × (1 + r + r2) = 16

a × (1 + 2 + (2)2) = 16

a × (1 + 2 + 4) = 16

a × (7) = 16

a =

The Sum of terms in G.P. is given by:

=

First term of the G.P is , common ratio of the G.P is 2 and Sum of n terms of the G.P is

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