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