Question

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.

Answer 1

Let the G.P. be a, ar, ar², ar³, … According to the given condition,
a + ar + ar² = 16 and ar³ + ar4 + ar⁵ = 128
⇒ a (1 + r + r²) = 16 ……………. (1)
ar³(1 + r + r²) = 128 …………….. (2)
Dividing equation (2) by (1), we obtain