Q. The sum of first four terms in a G.P. is 30 and that of the last four terms is 960.if its first term is 2 and last term is 512, find the common ratio.

Soln:

Let first term = a and last term = b of GP.

According to the given condition, the sum of first four terms is 30 i.e.

a + ar + ar^2 + ar^3 = 30

a (1 + r + r^2 + r^3) = 30

2 (1 + r + r^2 + r^3) = 30

(1 + r + r^2 + r^3) = 15 ..................eqn(i)

According to the second condition, the sum of last four terms is 960 i.e.

b/r^3 + b/r^2 + b/r + b = 960

b(1/r^3 + 1/r^2 + 1/r + 1) = 960

(1 + r + r^2 + r^3)/(r^3) = 960/512

15/r^3 = 1.875

r^3 = 15/1.875

r^3 = 8

r^3 = 2^3

r = 2 

Hence, common ratio is 2. Ans