Set up the characteristic equation, which is given by r2 − 5r − 6 = 0. The roots of this equation are given by r1 = 6 and r2 = −1. Thus a general solution for the recurrence is given by an = a6 n + b(−1)n . To find a and b, we use the initial conditions. a0 = 1 implies a + b = 1, while a1 = 3 implies 6a − b = 3.

Step-by-step explanation:

From your characteristic equation, your recursive equation is

the general solution:

The initial conditions are

For f(0) = 1, that is

For f(1) = 3, that is

From (*) and (**) you solve for A and B

you have A = 4/7 and B= 3/7

Replace A, B into the general one, you have the particular solution for the given condition