Solving With Iteration

Question

I have trouble proving the following with the iteration technique:

$T(n) = T(n-1) + 4n$

$T(n-1) = T(n-2) + 4n - 4$

$T(n-2) = T(n-3) + 4n - 8$

$T(n-3) = T(n-4) + 4n - 12$

What is the general form?

Answer 1

Hint:  $T_n \color{red}{- 2n^2} = T_{n-1} \color{red}{- 2n^2} +4n \color{red}{-2+2} = T_{n-1}-2(n-1)^2+2\,$, so $\,T_n-2n^2\,$ is an AP.