Find the sum of the indicated terms of the geometric sequence. $$\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$$
A) $\quad s = 192$
B) $s = 180$
C) $\quad s = 198$
D) $s = 186$
E) $s = 372$

Question

Quizplus · Accepted Answer

We can start by using the formula for the sum of the first $n$ terms of a geometric sequence: $$S_n = \frac{a(1-r^n)}{1-r},$$where $a$ is the first term and $r$ is the common ratio. Substituting in our values, we get $$\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 } = S_5 = \frac{6(1 - 2^5)}{1-2} = 6(2^5-1) = 186.$$Therefore, the answer is $\boxed{	ext{(D)}}$.

Find the Sum of the Indicated Terms of the Geometric ∑n=1n=56(2)n−1\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }n=1∑n=5​6(2)n−1

Find the Sum of the Indicated Terms of the Geometric $\sum _ { n = 1 } ^ { n = 5 } 6 ( 2 ) ^ { n - 1 }$