2020 VJC P1 Q6

The sequence \({{a}_{1}}\), \({{a}_{2}}\), \({{a}_{3}}\)… is a geometric progression \(A\) with common ratio \(\frac{3}{4}\), and the sequence \({{b}_{1}}\), \({{b}_{2}}\), \({{b}_{3}}\)… is an arithmetic progression \(B\). The sum to infinity of \(A\) is equal to the sum of the first ten terms of \(B\). Given that \({{a}_{1}}={{b}_{9}}+13\) and the sum of \({{a}_{2}}\) and \({{b}_{2}}\) is \(35.825\), find \({{a}_{1}}+{{a}_{2}}+{{a}_{3}}+...+{{a}_{25}}\), giving your answer correct to \(2\) decimal places.