Question

Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 8 terms and select the correct answer below.

a.) –195,312
b.) 195,312
c.) 292,968
d.) –292,968

I need help i had solved this question and i got the answer b but i want to make sure i am correct.

Answer 1

Answer: Option 'B' is correct.

Explanation:

Since we have given that

–3, 15, –75, 375, …

here, a = first term = -3

r = common ratio is given by

`(a_2)/(a_1)=(15)/(-3)=-5`

Number of terms = n =8

As we know the "Sum of geometric sequence":

`a_n=(a(r^n-1))/(r-1)\\\\a_8=(-3(-5^8-1))/(-5-1)\\\\a_8=-3(390625-1)}{-6}\\\\a_8=195,312`

Hence, Option 'B' is correct.