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

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 $T_{n+1}$?