Question

Find the sum of a finite geometric sequence from n = 1 to n = 6, using the expression −2(5)n − 1.

A. 1,223
B. −1,023
C. 7,812
D. −7,812

Answer 1

`\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ 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=n^(th)\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-2\\ r=5\\ n=6 \end{cases} \\\\\\ S_6=-2\left( \cfrac{1-5^6}{1-5} \right)`

Answer 2

The answer is D. −7,812