Answer: [tex]S_{12}=399.90[/tex]
Step-by-step explanation:
You know that the formula to find the sum of a finite geometric series is:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Where [tex]n[/tex] is the number of terms, [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio ([tex]r\neq 1[/tex]).
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:
[tex]r=\frac{a_2}{a_1}[/tex]
Then:
[tex]r=\frac{100}{200}\\\\r=\frac{1}{2}[/tex]
2. Finally, knowing that:
[tex]a_1=200\\\\n=12[/tex]
You must substitute values into the formula.
Then you get:
[tex]S_{12}=\frac{200(1-(\frac{1}{2})^{12})}{1-\frac{1}{2}}\\\\S_{12}=399.90[/tex]
