2026 CJC Promo Q6

An arithmetic progression has first term \(a\) and common difference \(d\), where \(a\) and \(d\) are non-zero. A convergent geometric progression has common ratio \(r\).

The first, fourth and sixth term of the arithmetic progression are the first three terms of the geometric progression respectively.

1. Show that \(r=\dfrac23\).[3]
2. Given that the sum to infinity of the geometric progression is \(9\), find the values of \(a\) and \(d\).[2]
3. Find the least value of \(n\) such that the sum of the first \(n\) terms of the arithmetic progression exceeds the sum of the first \(n\) terms of the geometric progression by at least \(5\).[3]