Sequences in Sequences

Question

How would you find the sum of the sequence:

0,4,12,24,40,60,...,760

whose terms increase based on the arithmetic sequence:

4,8,12,...

It seems similar to triangular numbers.

How would you find the sum of these sequences in general? (e.g. 5,7,12,20,31... whose terms increase based on the arithmetic sequence 2,5,8,11,...)

Answer 1

5320

a2-0 =4

a3-a2=8

..............

760-an-1=4+4(n-2)

If you add you get 760 = (4+4+4(n-2))(n-1)/2

2n^2-2n = 760, n = 20

Sum (2n^2+2n)=2n(n+1)(2n+1):6 +2n(n+1)/2 for n=20 we get 5320