What is the n-th term of the sequence 2, 6, 12, 20...?
Answer Details
The given sequence is formed by adding consecutive even numbers starting from 2. The first term is 2, the second term is 2 + 4, the third term is 2 + 4 + 6, and so on.
Thus, we can observe that the n-th term is obtained by adding the first n even numbers. The sum of the first n even numbers is n(n+1), which can be proved using mathematical induction.
Therefore, the n-th term of the sequence is n(n+1).
Hence, the correct option is: n2 + n.