2026 IGCSE Additional Mathematics May/June 0606/12 Q10

It is given that a geometric progression has the following terms.

2nd term: \(11x-1\)

3rd term: \(x+5\)

4th term: \(x-1\)

1. Given that \(x>0\), find the common ratio and first term of the progression.[6]
2. The sum to infinity of this progression is \(\dfrac k3\) where \(k\) is an integer.
   Find the value of \(k\).[2]