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

That is what i got but i got it right

Answer 2

Answer: Option 'B' is correct.

Step-by-step explanation:

Since  we have given that

–3, 15, –75, 375, …

here, a = first term = -3

r = common ratio is given by

$\frac{a_2}{a_1}=\frac{15}{-3}=-5$

Number of terms = n =8

As we know the "Sum of geometric sequence":

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

Hence, Option 'B' is correct.