Sunday

January 25, 2015

January 25, 2015

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

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 1:05pmThere 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 3:33pmSorry 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= -...

Algebra 2 - The sequence is defined by a recursion formula.Write the first four ...

7th grade math help Ms. Sue - 3. Which of the following equations has an ...

math - A sequence is generated by the recurrence relation Ur+1 = 1/Ur -3. Given ...

math - Seek power series solution of the given differential equation about the ...

Mathforme - 5. 4x + 2 = x + 8. (1 point) x = 4 x = 3 x = 2 x = 1 Solve the ...

kbMath - 5. 4x + 2 = x + 8. (1 point) x = 4 x = 3 x = 2 x = 1 Solve the ...

Math - Solve the linear programming problem by the method of corners. Minimize C...

7th grade math Ms. Sue please - 1. 5h – 9 = –16 + 6h (1 point) 4 –7 7 10 2. 4x...