Calculus 2 Recurence

Question

Solve the recurrence relation an =  2⋅an−1+3 with a0=1 

Answer 1

The characteristic equation is r-2.

The solution to the homogeneous equation is A*2ⁿand the general solution is a_n=A*2ⁿ-3.

The particular solution (from the initial condition) is a_n=2ⁿ⁺²-3.