A geometric series has first term \(a\) and common ratio \(r\), where \(|r|<1\). The sum to infinity of the series is \(8\). The sum to infinity of the series obtained by adding all the off-numbered terms (i.e. 1st term + 3rd term + 5th term + …) is \(6\). Find the value of \(r\).

We know the terms of the series we are given form a geometric series.

What can we say about the series formed by taking the odd-numbered terms instead?