Okay, so if you look at the sequence, we notice that they are alternating negative and positive. Also, we see that the absolute values of the numbers are increasing.
So, just ignore the negative and positives and look at the absolute values of these numbers:
2, 6,12,20, 30
let's check the factors:
1x2, 2x3, 3x4, 4x5, 5x6
So we see that the factors are increasing by 1;
n(n+1) depending on the value of n
so, for n = 1, n(n+1) = 1x2 = 2
for n=2, n(n+1) = 2x3 = 6, etc.....
so the sequence seems to be:
an = (-1)n x n(n+1)