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`.

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.