if the second and fourth terms of a GP 8 and 32 respectively what is the sum of the first four terms?​

Answer 1

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

Then, the second term is ar, the third term is ar^2, and the fourth term is ar^3.

We are given that the second term (ar) is 8 and the fourth term (ar^3) is 32.

So, we can write two equations:

ar = 8

ar^3 = 32

Dividing the second equation by the first, we get:

r^2 = 4

r = 2 or r = -2

If r = 2, then a = 4 (from the first equation).

So, the first four terms of the GP are:

4, 8, 16, 32

The sum of these terms is:

4 + 8 + 16 + 32 = 60

If r = -2, then a = -4 (from the first equation).

So, the first four terms of the GP are:

-4, 8, -16, 32

The sum of these terms is:

-4 + 8 - 16 + 32 = 20

Therefore, the sum of the first four terms of the GP is either 60 or 20, depending on the value of the common ratio.