Let the first term of the geometric progression be \(a\) and the common ratio be \(r\).

The second term is given by \(ar = 48\).

The third term is given by \(ar^2 = 32\).

Dividing the third term by the second term gives:

\(\frac{ar^2}{ar} = \frac{32}{48}\)

\(r = \frac{2}{3}\)

Substitute \(r = \frac{2}{3}\) into \(ar = 48\):

\(a \left( \frac{2}{3} \right) = 48\)

\(a = 72\)

The sum to infinity of a geometric progression is given by:

\(S_\infty = \frac{a}{1 - r}\)

Substitute \(a = 72\) and \(r = \frac{2}{3}\):

\(S_\infty = \frac{72}{1 - \frac{2}{3}} = \frac{72}{\frac{1}{3}} = 72 \times 3 = 216\)