Question

What is the nth term of the sequence below?

2, 6, 12, 20, . . .

3n

n^2 - 1

n^2 + 1

n (n+ 1)

Answer 1

n(n+1)

Explanation:

Only the last two formulas work for n=1; only the last formula works for n=2.

For n=1

3n = 3 ≠ 2

n² -1 = 0 ≠ 2

n² +1 = 2

n(n+1) = 2

For n=2

n²+1 = 5 ≠ 6

n(n+1) = 6 . . . . . this last formula works for the given sequence