Posted by **Francesca ** on Tuesday, April 5, 2011 at 11:16am.

Solve the recurrence relation a_n = -2a_n-1 + 15a_n-2, 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?

## Answer this Question

## Related Questions

- Discrete Math - Solve the recurrence relation a_n = -6a_n - 1 + 7a_n-2, n ≥...
- math - -Write the arithmetic sequence 21,13,5,-3... in the standard form: a_n= -...
- Calculus - If a_n>0 and a_(n+1) <= a_n, does the alternating series ∑...
- Calculus - If a_n does not equal zero for any n>=1 and ∑a_n converges ...
- Algebra - For the following sequences determine the term indicated: a_1=-2, a_n=...
- Calculus - Find a series ∑a_n for which ∑(a_n)^2 converges but &#...
- Algebra 2 - The sequence is defined by a recursion formula.Write the first four ...
- Algebra - find the arithmetic mean A_n-1_-3.9, A_n+1_=7.1
- Math Proof - 0<=b_n<=a_n. a) if a_n-->0 then b_n-->0. b) if a_n-->...
- Calculus - If a_n >0 and b_n >0 and series ∑ sqrt( (a_n)^2 +(b_n)^2...

More Related Questions