If the initial conditions are changed to y₀ = 1 and y₁ = 2 for the Fibonacci sequence in Exercise 17, list the terms of the sequence for k = 2, 3, 4 and 5. Find the solution to the difference equation from 17 with these new initial conditions.

Data from in  Exercise 17

The Fibonacci Sequence is listed in Table 1 of Section 4.7. It can be viewed as the sequence of numbers where each number is the sum of the two numbers before it. It can be described as the homogeneous difference equation

with the initial conditions y₀ = 0 and y₁ = 1. Find the general solution of the Fibonacci sequence.

Data from in Table 1

Yk+2 Yk+1 Yk = 0 -