# Math Help - homogeneous recurrence

1. ## homogeneous recurrence

I've come this far:

an = 4an-1 + 5an-2

a1 = 2
a2 = 6

roots
x1 = 5
x2 = -1

I insert roots in : an = U*s1^n + V*s2^n

which gives : an = 4*5^n + 5*(-1)^n

what now?

an could e.g. be a1?

I've come this far:

an = 4an-1 + 5an-2

a1 = 2
a2 = 6

roots
x1 = 5
x2 = -1

I insert roots in : an = U*s1^n + V*s2^n Correct, except that you mean x1 and x2 - see below

which gives : an = 4*5^n + 5*(-1)^n No

what now?

an could e.g. be a1?
Thanks for showing us your working so far. What you mean is:

$a_n = U{x_1^n} + V{x_2^n} = U.5^n +V.(-1)^n$

Then plug in the values $n = 1, n = 2$:

$a_1 = 2= 5U -V$

$a_2 = 6 = 25U + V$

Can you complete it now?