Question

***medal***
A geometric sequence starts with a1 = 3, and the common ratio is −2. What is the sum of the first 6 terms of the series?

Answer 1

\( {
\textit{sum of a finite sequence}=\sum\limits_{i=1}^{{\color{brown}{ 6}}}\implies S_{\color{brown}{ 6}}=a_1\left( \cfrac{1-r^{\color{brown}{ n}}}{1-r} \right)\qquad
\begin{cases}
a_1=3\\
r=-2
\end{cases}
\\ \quad \\
S_{\color{brown}{ 6}}=3\left( \cfrac{1-(-2)^{\color{brown}{ 6}}}{1-(-2)} \right)
}\)