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]

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.

2020 RI P2 Q1

2020 RI P2 Q1

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