Hello Siew.

Whenever I am faced with a sequence, I first look at the differences
between the terms:

6 - 3 = 3
12 - 6 = 6
21 - 12 = 9
33 - 21 = 12
etc.

Aha! A pattern has emerged. Each difference is 3 more than the last difference.

We can write it like this:

3 = 3
6 = 3 + 1(3)
12 = 3 + 1(3) + 2(3)
21 = 3 + 1(3) + 2(3) + 3(3)
33 = 3 + 1(3) + 2(3) + 3(3) + 4(3)

and write in general:

nth term = 3 + 1(3) + 2(3) + ... (n-1)(3).

By factoring, we get 3[1 + (1 + 2 + ... n-1) ]

The inside parentheses are a well-known sum - can you look it up and replace what's in those inner parentheses with a simpler formula without an ellipsis (...)?

Hope this helps,
Stephen La Rocque.