-12 + -12 + -10 + -6 + 0 + 8 + 18 + 30 + .... gives the sums

-12

-24

-34

-40

-40

-32

-14

16 which you could get using the formula S(n) = n^3 / 3 - n^2 - 34n/3

sum(j = 1 to n) (j^2 - 3j - 10) = sum(j = 1 to n) j^2 - 3 sum(j = 1 to n) j - 10 sum(j = 1 to n) 1

For the first term, insert a formula for the sum of j^2 from 1 to n.

For the second term, insert a formula for the sum of j from 1 to n.

For the third term, it's just 10 *1.