The triangular sequence has first term of 1, second term of 1 + 2, third term of 1 + 2 + 3, and so on. This is called a triangular sequence because one can represent the sequence as a triangle of dots.

The term to term rule is that the next term value is the current term + (the difference between the current term and previous term) + 1. Knowing this rule, you can generate further terms of the sequence just knowing 2 previous terms. Also, at position n, the term is the sum of the first n numbers 1 + 2 + … + n.

The nth term of the triangular sequence is the sum of the first n natural numbers 1 + … + n, which is equal to n(n+1)/2.

1

What is the next term of the triangular sequence 1, 3, 6, …? Recall the last term 6, represented as a triangle of dots.

2

What is 3rd term of the triangular sequence?

3

What is the 12th term of the triangular sequence?

4

Is 3, 6, 10, 15 a part of the triangular sequence?

5

Give the triangular sequence up to the 8th term.