2020 VJC Promo Q7

An infinite geometric series has first term \(a\) and common ratio \(r\), where \(r>0\). The third term is \(36\) and the sum to infinity is \(243\)

1. Find the value of \(a\) and \(r\).[3]

An arithmetic series has first term \(1\) and common difference \(d\). The sum of the first \(6\) terms of the arithmetic series is equal to the sum of the first \(3\) terms of the geometric series.

2. Find the value of \(d\).[3]
3. Find the least value of \(n\) for which the \({{n}^{\mathrm{th}}}\) term of the arithmetic series is more than the sum of the first \(2n\) terms of the geometric series.[3]