## 'Triangles Within Triangles' printed from http://nrich.maths.org/

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 $T_{n+1}$?