Question

HELP ASAP PLEASE!!! 20 POINTS!!

Answer 1

Answer: $S_{12}=399.90$

Step-by-step explanation:

You know that the formula to find the sum of a finite geometric series is:

$S_n=\frac{a_1(1-r^n)}{1-r}$

Where $n$ is the number of terms, $a_1$ is the first term and $r$ is the common ratio ($r\neq 1$).

The steps to find the sum of the first 12 terms of the given geometric serie, are:

1. Find the common ratio "r". By definition:

$r=\frac{a_2}{a_1}$

Then:

$r=\frac{100}{200}\\\\r=\frac{1}{2}$

2. Finally, knowing that:

$a_1=200\\\\n=12$

You must substitute values into the formula.

Then you get:

$S_{12}=\frac{200(1-(\frac{1}{2})^{12})}{1-\frac{1}{2}}\\\\S_{12}=399.90$