# Math Help - what is a triangular number ?

1. ## what is a triangular number ?

what is a triangular number ????

A triangular number is the sum of the n natural numbers from 1 to n. The sequence of triangular numbers for n = 1, 2, 3... is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ....

3. Hello, sportychick1912!

What is a triangular number?

They arise from triangular arrays of objects.
Code:
                                              o
o           o o
o         o o         o o o
o       o o       o o o       o o o o
o     o o     o o o     o o o o     o o o o o

1      3        6         10           15

And we have:

. . $\begin{array}{ccccc}T_1 &=& 1 &=& 1 \\
T_2 &=& 1+2 &=& 3 \\ T_3 &=&1+2+3 &=& 6 \\ T_4 &=&1+2+3+4 &=&10 \\ T_5 &=& 1+2+3+4+5 &=&15 \\ \vdots & & \vdots & & \vdots \\
T_n &=& 1+2+3+\hdots+n &=&\dfrac{n(n+1)}{2}\end{array}$