The second term of a geometric progression is \(24\), and the fifth term is \(\frac{8}{9}\).
Calculate the first term, the common ratio and the sum to infinity, if it exists.
A second series is formed by squaring each term of the given geometric progression. Find the sum to infinity of this second series, justifying its convergence.

The second term of a geometric progression is \(24\), and the fifth term is \(\frac{8}{9}\).

Calculate the first term, the common ratio and the sum to infinity, if it exists.

A second series is formed by squaring each term of the given geometric progression. Find the sum to infinity of this second series, justifying its convergence.

Example of sum to infinity

Example of sum to infinity