May/June 2026 Paper 12

The second, fourth and last terms of an arithmetic progression are $60$, $52$ and $-28$ respectively. Find the sum of all of the terms in the progression.

The second, third and fourth terms of a geometric progression are $9$, $k+4$ and $k^2$ respectively, where $k$ is a negative constant.

Find the value of $k$.

Find the sum to infinity of the progression.