2025 IGCSE Additional Mathematics February/March 0606/12 Q8

The first term of a geometric progression is \(10\).

This geometric progression has a positive common ratio \(r\).

The first term of an arithmetic progression is also \(10\).

This arithmetic progression has a negative common difference \(d\).

The second term of the geometric progression is the same as the fourth term of the arithmetic progression.

The third term of the geometric progression is the same as the sixth term of the arithmetic progression.

1. Find the values of \(r\) and \(d\).[6]
2. Determine whether the geometric progression has a sum to infinity.[1]