Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first 9 terms of the geometric sequence: $\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 } , \frac { 16 } { 5 } , \ldots$
A) $\frac { 511 } { 5 }$
B) $\frac { 509 } { 5 }$
C) $\frac { 518 } { 5 }$
D) 101

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = \frac{1}{5}$, $r = 2$, and $n = 9$. Plugging these values into the formula gives $S_9 = \frac{\frac{1}{5}(1 - 2^9)}{1 - 2} = \frac{\frac{1}{5}(1 - 512)}{-1} = \frac{511}{5}$.

Use the Formula for the Sum of the First N 15,25,45,85,165,…\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 } , \frac { 16 } { 5 } , \ldots51​,52​,54​,58​,516​,…

Use the Formula for the Sum of the First N $\frac { 1 } { 5 } , \frac { 2 } { 5 } , \frac { 4 } { 5 } , \frac { 8 } { 5 } , \frac { 16 } { 5 } , \ldots$