If the second and fourth terms of a G.P are 8 and 32 respectively, what is the sum of the first four terms?

Answer 1

Let the first term of the G.P be 'a' and the common ratio be 'r'.

We know that the second term is ar, and the fourth term is ar^3.

Given that the second term is 8 and the fourth term is 32:

ar = 8

ar^3 = 32

Dividing the second equation by the first equation:

(ar^3)/(ar) = 32/8

r^2 = 4

r = 2 or r = -2

If r = 2, then a = 4 (from ar = 8).

If r = -2, then a = -4 (from ar = 8).

So the G.P can be either 4, 8, 16, 32 or -4, 8, -16, 32.

In either case, the sum of the first four terms is:

4 + 8 + 16 + 32 = 60

or

-4 + 8 - 16 + 32 = 20

Therefore, the sum of the first four terms is either 60 or 20, depending on the sign of the first term.