if the answer includes a variable to the power of 2, it is most likely a quadratic sequence.
the general formula for a quadratic sequence is u_n = an^2+bn+c
0, 2, 6, 12, 20, 30, 42
2, 4, 6, 8, 10, 12 (d_1)
2, 2, 2, 2, 2 (d_2)
the second difference is constant.
in an^2+bn+c, a = d_2/2
a = 2/2 = 1
this means that u_n = n^2+bn+c
b and c can be found by comparing the sequence in question with the sequence u_n = n^2, since a is the same for both of them.
u_n = n^2+bn+c:
0, 2, 6, 12, 20
u_n = n^2:
1,4,9,16,25
then, subtract the numbers in u_n = n^2 from u_n = n^2+bn+c:
0-1 = -1
2-4 = -2
6-9= -3
12-16 = -4
subtracting n^2 from u_n = n^2+bn+c gives us bn+c, which is a linear sequence.
-1, -2, -3, -4...
the nth term here is -n.
this means that bn+c = -n
-n is the same as -n +0, which gives c as 0, and b as -1.
finally, a= 1, b=-1, c=0
an^2+bn+c = n^2-n
u_n = an^2+bn+c = n^2-n