Posted by Francesca on Tuesday, April 5, 2011 at 11:16am.
Solve the recurrence relation a_n = 2a_n1 + 15a_n2, n ≥ 2, given a₀ = 1, a₁ = 1.
x² + 2x  15, the distinct roots 3 and 5, so a_n = C₁(3^n) + C₂(5)^n. The initial condition gives a₀ = 1 = C₁  C₂, a₁ = 1 = 3C₁  5C₂. We obtain C₁ = C₂ = 1/2 and so a_n = 1/2(3^n) + 1/2(5)^n.
My question is how does C₁ = C₂ = 1/2 can some please how do you derive to this answer because I'm confused.Thank you for any help.

Discrete Math  Count Iblis, Tuesday, April 5, 2011 at 1:05pm
There wasa typo in the equations derived from the initial conditions. You should have:
The initial condition gives
a₀ = 1 = C₁ + C₂,
a₁ = 1 = 3C₁  5C₂
It then easily follows that
C₁ = C₂ = 1/2

Discrete Math  Francesca, Tuesday, April 5, 2011 at 3:33pm
Sorry I still don't get it. Can someone please explain?
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