Question

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

Answer 1

the first term is −11

the last term is −45,056

the common ratio is −4

the formula for geometric series is

`\begin{gathered} a+ar+ar2+ar3+\ldots \\ \sum ^n_1a_1r^(n-1) \\ \text{solution formula:} \\ S_n=a_1(1-r^n)/(1-r) \end{gathered}`

where

r = -4

a1 = -11

n = 7

therefore,

`S_7=(-11)(1-(-4)^7)/(1-(-4))`

let's simplify

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

Thus, the answer is -36047