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What is the sum of a 7-term geometric series if the first term is −11, the last term is −45,056, and the common ratio is −4? A −143,231B −36,047C 144,177D 716,144

Sagot :

the first term is −11

the last term is −45,056

the common ratio is −4

the formula for geometric series is

[tex]\begin{gathered} a+ar+ar2+ar3+\ldots \\ \sum ^n_1a_1r^{n-1} \\ \text{solution formula:} \\ S_n=a_1\frac{1-r^n}{1-r} \end{gathered}[/tex]

where

r = -4

a1 = -11

n = 7

therefore,

[tex]S_7=(-11)\frac{1-(-4)^7}{1-(-4)}[/tex]

let's simplify

[tex]\begin{gathered} S_7=(-11)\frac{1-(-4)^7}{1-(-4)}=-11\cdot\frac{1-(-16384)}{1+4}=-11\cdot\frac{1+16384}{1+4}=-11\cdot\frac{16385}{5} \\ S_7=-11\cdot\: 3277 \\ S_7=-36047 \end{gathered}[/tex]

Thus, the answer is -36047

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