Please show me how to simplify this recurrence relation

[s3a]

I'm doing a much larger problem and I am stuck going from:

T(n) = 14 + T (n − 2) + 10(n + (n − 1))
to
T(n) = (n − 1)7 + T(1) + 10(Σi=2 to n of i)

and I would very much appreciate it if someone could show me the detailed steps. (I've been told something about expanding the recursive functions but I'm having a lot of trouble doing it.)

Thanks in advance!

 

[tiny-tim]

hi s3a!

T(n) = 14 + T (n − 2) + 10(n + (n − 1))

so T(n) - T (n − 2) = 14 + 10(n + (n − 1))

so T(n) - T (1) = … ?

 

[NascentOxygen]

Are you sure that 7 shouldn't be 14?

EDIT: My mistake. 7 is correct.

 

[s3a]

I'm not sure of anything. That's what my sheet says.

Also, for the T(n) - T(n - 2) = ... thing, do I plug in n = 3? Or is that not what I am supposed to do?

 

[tiny-tim]

If T(11) - T(9) = ... thing,

T(9) - T(7) = ... thing,

…

what is T(11) - T(1) ? ​