Find the sum of the geometric series, if possible.
-$$\sum _ { n = 1 } ^ { 9 } 5 ( 2 ) ^ { n }$$
A) 5,110
B) 2,550
C) 1,022
D) 2,555

Question

Quizplus · Accepted Answer

The sum of a geometric series can be found using the formula $$S = \frac{a(1 - r^n)}{1 - r}$$, where $S$ is the sum of the series, $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. In this series, the first term $a = 5(2)^1 = 10$, the common ratio $r = 2$, and there are $n = 9$ terms. Plugging these values into the formula gives $$S = \frac{10(1 - 2^9)}{1 - 2} = \frac{10(1 - 512)}{-1} = \frac{-10 \times -511}{1} = 5,110.$$

Find the Sum of the Geometric Series, If Possible ∑n=195(2)n\sum _ { n = 1 } ^ { 9 } 5 ( 2 ) ^ { n }n=1∑9​5(2)n

Find the Sum of the Geometric Series, If Possible $\sum _ { n = 1 } ^ { 9 } 5 ( 2 ) ^ { n }$