Question

Find the sum of the n terms of the series `1*4*7 + 2*5*8 + 3*6*9.....`?

Answer 1

`n^3+9n^2+18n`

Explanation:

Each term can be represented by:

`[n* (n+3)*(n+6)]`

Check:
second term: n = 2

`(2* (2+3)*(2+6)) => (2*5*8)`

Expand:

`[n* (n+3)*(n+6)]=> n^3+9n^2+18n`

nth term `n^3+9n^2+18n`

Sum of n terms:

`1/4n(n+7)(n+6)(n+1)`