Hello, Tangera!

Another challenging problem . . .

The first 3 terms of a G.P. are the 16th, 4th and 1st terms of an A.P.

Find the ratio of the sum to infinity for the G.P. to its first term.

For the G.P., let = first term, = common ratio.

For the A.P., let = first term, = common difference.

We have: .

Substitute into [4]: .

The G.P. has the sum: .

Therefore, the ratio is: .