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

The sum of infinite series whose first term ${a}_{1} = 18$ and $r = 0.6$ is $45$.
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 ${a}_{1} / \left(1 - r\right)$.
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