Question

Find the first four terms of the following recurrence relationship: Un+2=2Un+1+Un, U1=3, U2=5

Answer 1

If we use U1 and U2 we can work out U3 by substituting U1 for Un and U2 for Un+1

U3 = 2*5 + 3 = 13

We can do the same for U4:
U4 = 2*13 + 5 = 31

Therefore:
U1 = 3
U2 = 5
U3 = 13
U4 = 31