2020 RI P2 Q1

An arithmetic series has first term \(\frac{3}{2}\) and fourth term \({{u}_{4}}\).

A geometric series also has first term \(\frac{3}{2}\) and fourth term \({{u}_{4}}\).

Given that the common ratio of the geometric series is non-negative and the sum of its first \(3\) terms is \(\frac{21}{2}\), find the sum of the first \(10\) odd-numbered terms of the arithmetic series.[5]