The formula for the sum to infinity of a geometric progression is \(\frac{a}{1-r}\), where \(a\) is the first term and \(r\) is the common ratio.

Given that the sum to infinity is equal to eight times the first term, we have:

\(\frac{a}{1-r} = 8a\)

Dividing both sides by \(a\) (assuming \(a \neq 0\)) gives:

\(\frac{1}{1-r} = 8\)

Solving for \(r\), we get:

\(1 = 8(1-r)\)

\(1 = 8 - 8r\)

\(8r = 7\)

\(r = \frac{7}{8}\)