What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?

Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

S5 = −136

S5 = −33

S5 = 12

S5 = 33

Question

What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?

Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

 S5 = −136

 S5 = −33

 S5 = 12

 S5 = 33

data_lg2 · Answer

Sum of geometric series for the first n-terms are given by

$\sf \Large \sf S_n=a_1 ( \frac{1-r^n}{1-r}) $

where $\sf a_1$ is the first term and $\sf r$ is the ratio between the terms.  

You are given $\sf a_1=3$ and $\sf r= -2$, substitute these values in the formula and what will you get?