Question

Let {an} be a sequence that satisfies the recurrence relation an=anà ƒ ƒ ¢ ˆ ’1+3anà ƒ ƒ ¢ ˆ ’2, for n=2,3,.,.,., where a0=1,a1=2. Find the values of a2,a3.

Answer 1

$$a_n=a_{n-1}+3a_{n-2}, n\geq2$$

$a_0=1, a_1=2$

$$a_2=a_1+3a_0=2+3(1)=5$$

$$a_3=a_2+3a_1=5+3(2)=11$$