Find the sum of the finite geometric sequence.(Round your answer to three decimal places.) $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$
A)2,092.596
B)1,691.128
C)340.518
D)352.212
E)1,312.385

Question

Find the sum of the finite geometric sequence.(Round your answer to three decimal places.)   $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$  
A)2,092.596
B)1,691.128
C)340.518
D)352.212
E)1,312.385

Quizplus · Accepted Answer

The sum of a finite geometric sequence can be found using the formula $S = \frac{a(1 - r^n)}{1 - r}$, where $S$ is the sum of the sequence, $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. In this case, $a = 300$, $r = 1.06$, and $n = 6$ (since the sequence starts from $n = 0$ and goes up to $n = 5$, making 6 terms in total). Plugging these values into the formula gives $S = \frac{300(1 - (1.06)^6)}{1 - 1.06}$, which calculates to approximately 2,092.596.

Find the Sum of the Finite Geometric Sequence ∑n=05300(1.06)n\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }∑n=05​300(1.06)n

Find the Sum of the Finite Geometric Sequence $\sum _ { n = 0 } ^ { 5 } 300 ( 1.06 ) ^ { n }$