Question

Solve a0 = 1, and an = 2an−1 + 1 for n ≥ 1 using the characteristic equation method. hint: try an = a, a constant, to find a particular solution.

Answer 1

Given that an=2an-1, to solve for a0=1, we substitute the value of a0 in the equation as follows:
a0=2*1-1+1
a0=2-1+1
a0=3-1
a0=2
the answer is 2