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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
C. 144,177
D. 716,144

Respuesta :

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:  [tex]a_{1}[/tex]=-11

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

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

                                     =-11×[tex]\frac{1-(-4)^{7} }{1-(-4)}[/tex]

                                     = [tex]\frac{-180235}{5}[/tex]

                                      = -36047

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