Question

How do you find the sum of the infinite geometric series given `a_1=18` and r=0.6?

Answer 1

The sum of infinite series whose first term `a_1=18` and `r=0.6` is `45`.

Explanation:

Sum of the infinite geometric series whose first term is `a_1` and common ratio `|r|<1` (only such series converge to a definite sum) is given by `a_1/(1-r)`.

Hence, the sum of infinite series whose first term `a_1=18` and `r=0.6` is

`18/(1-0.6)=18/0.4=(18×10)/4=45`