Question

Consider the sequence an = 6an−1 −9an−2 for n ≥ 2 , and a0 = 5 , a1 = 18. Use strong induction to prove that an = (n + 5)3n for all nonnegative integers n. Divide your work into the following parts.(a) base case(s) (b) inductive step including i. state the induction hypothesis ii. state the claim that you wish to prove (using the hypothesis) iii. complete the inductive step by proving your claim.

Answer 1

Incorrect information.

Explanation:

According to the information of the problem we have that

`a_n = 6a_(n-1) - 9a_(n-2)`

`a_0 = 5 \,\,\, , a_1 = 18`

Notice that if

`a_n = (n+5)3n`

in fact

`a_2 = 6a_1 - 9a_0 = 6(18)-9(5) = 63`

and if you explicit formula you are given then

`a_2 = (2+5)3(2) = 42.`

Therefore the base step is incorrect. And you can not proceed.