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 : .
The G.P. has the sum: .
Therefore, the ratio is: .