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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
C144,177
D716,144

Verified Answer :

irspow

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:  -36047

Step-by-step explanation:  \(a_{1}\)=-11

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

sum of geometric series= \(\frac{a_{1}(1-r^{n} ) }{1-r}\)

                                     =-11×\(\frac{1-(-4)^{7} }{1-(-4)}\)

                                     = \(\frac{-180235}{5}\)

                                      = -36047

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