Question

What is the sum of a 7 term geometric series if the first term is -11 and the last term is -45,056, and the common ratio is -4?

A. -143,231
B. -36,047
C. 144,177
D. 716,144

Answer 1

This sequence is:

a(n)=-11(-4)^(n-1)

The sum of the sequence is:

s(n)=-11(1--4^n)/(1--4)

s(n)=-11(1--4^n)/5

so for the first seven terms

s(7)=-11(1--4^7)/5

s(7)=-11(1+16384)/5

s(7)=-11(16385)/5

s(7)=-36047 B.

Answer 2

Answer: -36047

Step-by-step explanation:
`a_(1)`=-11

r=common ratio= -4 and n=number of terms=7

sum of geometric series=
`(a_(1)(1-r^(n) ) )/(1-r)`

=-11×
`(1-(-4)^(7) )/(1-(-4))`

=
`(-180235)/(5)`

= -36047