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
