Hello, puggie!

The sum to infinity of a geometric progression is 5, and the sum to infinity

of another series formed by taking the 1st, 4th, 7th, 10th, ... is 4.

Find the common ratio of the first series.

Answer: .

Why is rejected as an answer? . . To converge,

The first series has first term and common ratio

. . Its sum is: .

The second series has first term and common ratio

. . Its sum is: .

Equate and : .

. . which factors: .

. . and has roots: .

And only qualifies as a common ratio for a convergent series.