## Calculus with Applications (10th Edition)

$${S_5} = - 1705$$
\eqalign{ & {\text{the sum of the first }}n{\text{ terms of a geometric sequence}}{\text{ is given by}} \cr & {S_n} = \frac{{{a_1}\left( {{r^n} - 1} \right)}}{{r - 1}},{\text{ where }}r \ne 1 \cr & {\text{let }}n = 5,\,\,\,{a_1} = - 5{\text{ and }}r = 4 \cr & {S_5} = \frac{{\left( { - 5} \right)\left( {{{\left( 4 \right)}^5} - 1} \right)}}{{4 - 1}} \cr & {\text{simplifying}} \cr & {S_5} = \frac{{\left( { - 5} \right)\left( {1023} \right)}}{3} \cr & {S_5} = - 1705 \cr}