Find the sum of the geometric series, if possible.
-$$10 + 2 + \frac { 2 } { 5 } + \frac { 2 } { 25 } + \frac { 2 } { 125 }$$
A) $\frac { 18 } { 125 }$
B) $\frac { 18 } { 155 }$
C) $\frac { 1562 } { 125 }$
D) $\frac { 16 } { 155 }$

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = 10$ and common ratio $r = \frac{1}{5}$. The sum of a finite geometric series can be found using the formula $S_n = \frac{a(1 - r^n)}{1 - r}$, where $n$ is the number of terms. Here, $n = 5$, so the sum is $S_5 = \frac{10(1 - (\frac{1}{5})^5)}{1 - \frac{1}{5}} = \frac{10(1 - \frac{1}{3125})}{\frac{4}{5}} = \frac{10 \cdot \frac{3124}{3125}}{\frac{4}{5}} = \frac{3124}{625} \cdot \frac{5}{4} = \frac{1562}{125}$.

Find the Sum of the Geometric Series, If Possible 10+2+25+225+212510 + 2 + \frac { 2 } { 5 } + \frac { 2 } { 25 } + \frac { 2 } { 125 }10+2+52​+252​+1252​

Find the Sum of the Geometric Series, If Possible $10 + 2 + \frac { 2 } { 5 } + \frac { 2 } { 25 } + \frac { 2 } { 125 }$