A sequence of numbers x₀, x₁,x₂,... is such that x₀ = 4 and, for each n 1, x_n = Kx_{n - 1} + 3, where K is some fixed number such that O < K < 1. Find an explicit expression for x_n in terms of n and K.

What is the limiting value of x_n as tends to infinity? For which values of K will the sequence increase? For which will it decrease? For which will it be constant?