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

The sum to infinity of a geometric progression is given by \(\frac{a}{1-r} = 20\).

The sum of the first two terms is \(a + ar = 12.8\).

We have two equations:

1. \(\frac{a}{1-r} = 20\)

2. \(a(1 + r) = 12.8\)

From equation 1, \(a = 20(1-r)\).

Substitute \(a = 20(1-r)\) into equation 2:

\(20(1-r)(1+r) = 12.8\)

\(20(1-r^2) = 12.8\)

\(20 - 20r^2 = 12.8\)

\(20r^2 = 7.2\)

\(r^2 = 0.36\)

\(r = 0.6\) (since \(r\) is positive)

Substitute \(r = 0.6\) back into \(a = 20(1-r)\):

\(a = 20(1-0.6)\)

\(a = 20 \times 0.4\)

\(a = 8\)