2. A geometric series has first term \(a\), where \(a \neq 0\), and common ratio \(r\). The sum to infinity of this series is 6 times the first term of the series.
- Show that \(r = \frac { 5 } { 6 }\)
Given that the fourth term of this series is 62.5
- find the value of \(a\),
- find the difference between the sum to infinity and the sum of the first 30 terms, giving your answer to 3 significant figures.