The first term of a geometric series is 18 and the sum to infinity of the series is 20.

Find, in its simplest form, the ratio of the nth term of the series to the sum of all the subsequent terms of the infinite series.

Sum to infinity = \(\frac{18}{1-r}\), so \(\frac{18}{1-r}=20 \)

Sum to n'th term = \(\frac{18(1-r^n)}{1-r}\), so sum of subsequent terms = \(20 - \frac{18(1-r^n)}{1-r}\)

n'th term = \(18r^{n-1}\)

Can you complete the problem from here?