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