Discover the nth Term and Sum of a Series: 12, 23, 60, 169, 494

[hav0c]

Homework Statement

Find the nth term and sum to n terms of the series 12,23,60,169,494..

Homework Equations

The Attempt at a Solution

well each term is the triple of the previous term minus some constant.
23=10*3-7
60=23*3-9
..
..
This way i am able to write the nth term as 3(t_n-1)-3-2n
and hence proceed to find a telescopic sum by rearrangement and adding.
but this method leaves me with a t_n+1 which i am unable to write
So how shud i proceed

 

[haruspex]

Find the nth term and sum to n terms of the series 12,23,60,169,494..

I guess you meant 10,23, ...

well each term is the triple of the previous term minus some constant.
23=10*3-7
60=23*3-9
..
..
This way i am able to write the nth term as 3(t_n-1)-3-2n
and hence proceed to find a telescopic sum by rearrangement and adding.
but this method leaves me with a t_n+1 which i am unable to write
So how shud i proceed

Please post your working as far as you got.
Can you solve the homogeneous recurrence relation?
To account for the extra -3-2n, just try adding a linear term with a couple of unknown constants. See if you can determine what those constants would need to be.