Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 2 / 1A / b / Solution

Eliminate the free constant by comparing consecutive values:Therefore an appropriate inhomogeneous linear recurrence isIts homogeneous part has solution $a{2}^n$, and $-n$ is a particular solution. A first-order linear recurrence relation has one arbitrary initial value, so this gives exactly the desired general solution.