## anonymous one year ago ***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?

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