Problem

(a) The first three terms of an arithmetic progression are $25$, $4p - 1$ and $13 - p$, where $p$ is a constant.

Find the value of the tenth term of the progression.

(b) The first three terms of a geometric progression are $25$, $4q - 1$ and $13 - q$, where $q$ is a positive constant.

Find the sum to infinity of the progression.