A sequence an is defined recursively by a15 a27 and an 3an1

A sequence {a_n} is defined recursively by a_1=5, a_2=7 and a_n = 3a_(n-1) -2a_(n-2) -2 for n>=3. Prove that a_n= 2n+3 for every positive integer n

Solution

Answer:

Our induction hypothesis gives us values for a_(n-1) n a_(n-2) ,we plug them in solving the equation and see a_n = 2n +3

3*(2*(n-1)+3)-2(2n-4+3)-2 =2n+3