10 The geometric progression \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) has first term 2 and common ratio \(r\) where \(r > 0\). It is given that \(\frac { 9 } { 2 } a _ { 5 } + 7 a _ { 3 } = 8\).
- Find the value of \(r\).
- Find the sum of the first 20 terms of the geometric progression. Give your answer correct to 4 significant figures.
\includegraphics[max width=\textwidth, alt={}, center]{d6976a4b-aecf-43f1-a3f2-bcad37d03585-14_2725_42_134_2008} - Find the sum to infinity of the progression \(a _ { 2 } , a _ { 5 } , a _ { 8 } , \ldots\).