Question

Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 9 terms and select the correct answer below.

Choices:
A. -976,563
B. 976,563
C. 1,464,843
D. 976,562

Answer 1

Answer: A. -976563

Explanation:

Sn=sum of the n terms of the geometric sequence.

a= the first term

r=the common ratio

n=numbers of terms.

Sn=a[(1-r^n)/(1-r)]

In this case:

a=-3

r=a₂/a₁=15/-3=-5

n=9

S₉=-3[(1-(-5)⁹) / (1-(-5))=

S₉=-3(1+1953125)/6)=

S₉=-3(1953126/6)=

S₉=-3(325521)

S₉=-976563

Answer 2

Sn=sum of the n terms of the geometric sequence.
a= the first term
r=the common ratio
n=numbers of terms.

Sn=a[(1-r^n)/(1-r)]

In this case:
a=-3
r=a₂/a₁=15/-3=-5
n=9

S₉=-3[(1-(-5)⁹) / (1-(-5))=
S₉=-3(1+1953125)/6)=
S₉=-3(1953126/6)=
S₉=-3(325521)
S₉=-976563

Answer: A. -976563