Question

What's the sum of an infinite geometric series if the first term is 156 and the common ratio is 2∕3?A) 234B) 208C) 468D) 260

Answer 1

The sum of an infinite geometric series is given by:

`\begin{gathered} S=(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=(2)/(3) \\ \\ \text{Substitute the values and we have} \\ S=(a)/(1-r) \\ S=(156)/(1-(2)/(3)) \\ S=(156)/((1)/(3)) \\ S=156\cdot3 \\ S=468 \end{gathered}`

Therefore, the sum of the infinite series with a first term of 156, and a common ratio of 2/3 is 468.