The sum of an infinite geometric series is given by:
[tex]\begin{gathered} S=\frac{a}{1-r} \\ \text{where} \\ a\text{ is the first term} \\ r\text{ is the common ratio} \\ \\ \text{The following are the given} \\ a=156 \\ r=\frac{2}{3} \\ \\ \text{Substitute the values and we have} \\ S=\frac{a}{1-r} \\ S=\frac{156}{1-\frac{2}{3}} \\ S=\frac{156}{\frac{1}{3}} \\ S=156\cdot3 \\ S=468 \end{gathered}[/tex]Therefore, the sum of the infinite series with a first term of 156, and a common ratio of 2/3 is 468.
