A geometric series is \(a + a r + a r ^ { 2 } + \ldots\)
Prove that the sum of the first \(n\) terms of this series is given by
$$S _ { n } = \frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$$
The third and fifth terms of a geometric series are 5.4 and 1.944 respectively and all the terms in the series are positive.
For this series find,