Question

Which of the below given sequences {an} is not a solution of the recurrence relation an = 8a n-1 - 16a n-2?
Please check first reply attachment.

Answer 1

wasn't able to write the question so check the attachment better.

Answer 2

Well, you can always pick an a_{n}, plug it in and check it. Like for example, if you were to test n4^n, you would get:
\[n4^{n} = 8(n-1)4^{n-1}-16(n-2)4^{n-2}\] and see if it's true. If its true, goto the next one and see.

Answer 3

@Concentrationalizing
Can you please tell me what exactly is the rule? or what's the true answer?
Because you mentioned a_{n} but you didn't used it at all.
Thanks.

Answer 4

Well all your options a, b, c, d are different \(a_{n}\)'s. So when I set up the problem using \(n4^{n}\), that was my \(a_{n}\). I wouldn't say there's an explicit rule for this problem, you just need to check your options. Using \(a_{n} = n4^{n}\), \(a_{n-1} = (n-1)4^{n-1}\), \(a_{n-2} = (n-2)4^{n-2}\), I plugged them into the recurrence relation you were given. Then I would just need to simplify and see if I get a true statement. You would need to do this substitution which each one of your possible choices until you find a false statement.