Question

Is an = -n + 2 a solution to an = an-1 +2an-2 + 2n-9

Answer 1

Answer:

Yes, $a_n=-n+2$ is a solution of $a_n=a_{n-1}+2a_{n-2}+2n-9$.

Step-by-step explanation:

Given

$a_n= a_{n-1}+2a_{n-2}+2n-9$

To prove that $a_n=-n+2$ is a solution of the given expression $a_n=a_{n-1}+2a_{n-2}+2n-9$

Take Right hand side :

$a-{n-1}+2a_{n-2}+2n-9$

Substitute the value of $a_n=-n+2$

Now , we get

-(n-1)+2+2{-(n-2)+2}+2n-9

=-n+1+2+2(-n+4)+2n-9 ( simplified)

=-n-6+8-2n+2n ( simplified )

=$-n+2 ( simplified)=a_n$

Hence, LHS=RHS

Therefore, $a_n=-n+2$ is a solution of given expression

$a_n=a_{n-1}+2a_{n-2}+2n-9$

Yes, $a_n=-n+2$ is a solution of given expression.