Question

What is the solution of the recurrence relation \[ a_n=6a_{n-1}-9a_{n-2} \] with initial conditions \[ a_0=1,\qquad a_1=6? \]

• A. \(a_n=3^n+n\times 3^n\)
• B. \(a_n=1-2^n+2\times 3^n\)
• C. \(a_n=2^n+3^n\)
• D. \(a_n=3^n\)

Hint:

For a repeated root \(r\) of multiplicity 2, the solution is \[ a_n=(C_1+C_2n)r^n. \] Always remember the extra factor \(n\) for repeated roots.

Answer 1

The Correct Option is A