Question

determine the sum of the first 8 terms of the geometric sequence if the first term is 5, the common ratio is -2 and the 8th term is -640​

Answer 1

-425

Explanation:

You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.

Series sum

The sum is given by the formula ...

Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio

The sum of 8 terms of the given series is ...

S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425

The sum of 8 terms is -425.