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

Let the three terms be a, ar, ar2.

a + ar + ar2 = 16 ………………………(i)

Let the next three terms be ar3, ar4, ar5.

ar3 + ar4 + ar5 = 128

r3(a + ar + ar2) = 128

r3(16) = 128 (from i)

r3 = 8

r = 2

Therefore the common ratio is 2.

Substituting r = 2 in (i)

a + 2a + 4a = 16

7a = 16

a = 16/7

Sn = Therefore the first term is 16/7, common ratio is 2 and sum to n terms is .

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