This diagram shows how the first triangular number can be added to 3 copies of the second triangular number to make the fourth triangular number:

That is:

T_{1} + 3 \times T_{2} = T_{4}

Here is a diagram showing how the second and third triangular numbers can be combined to make the sixth triangular number:

T_{2} + 3 \times T_{3} = T_{6}

Can you generalise this rule?

Can you find a rule in terms of $T_{n}$ and $T_{n + 1}$ ?