Question

What is the sum of a 7-term geometric series if the first term is -6, the last term is -24 576, and the common ratio is 4?​

Answer 1

`\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_(i=1)^(n)\ a_1\cdot r^(i-1)\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} a_1 = -6\\ r= 4 \end{cases} \\\\\\ S_7=-6\left(\cfrac{1-4^7}{1-4} \right)\implies S_7=-6\left( \cfrac{-16383}{-3} \right)\implies S_7=-32766`

and yes, we know the that the last -6*4⁶ = -24576, however we don't need it for the sum equation.