Answer:
Yes, [tex]a_n=-n+2[/tex] is a solution of [tex]a_n=a_{n-1}+2a_{n-2}+2n-9[/tex].
Step-by-step explanation:
Given
[tex]a_n= a_{n-1}+2a_{n-2}+2n-9[/tex]
To prove that [tex]a_n=-n+2[/tex] is a solution of the given expression [tex]a_n=a_{n-1}+2a_{n-2}+2n-9[/tex]
Take Right hand side :
[tex]a-{n-1}+2a_{n-2}+2n-9[/tex]
Substitute the value of [tex]a_n=-n+2 [/tex]
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 )
=[tex]-n+2 ( simplified)=a_n[/tex]
Hence, LHS=RHS
Therefore, [tex]a_n=-n+2[/tex] is a solution of given expression
[tex]a_n=a_{n-1}+2a_{n-2}+2n-9[/tex]
Yes, [tex]a_n=-n+2 [/tex] is a solution of given expression.
