What is a triangular number?

Answer 1

A triangular number is a member of the series which is calculated as follows:

t(1) = 1 = 1

t(2) = 1 + 2 = 3

t(3) = 1 + 2 + 3 = 6

t(4) = 1 + 2 + 3 + 4 = 10

and so on.

t(n) = 1 + 2 + 3 + 4 + ... + n

Fortunately, there is a simpler formula

t(n) = n*(n+1)/2

To see why they are called triangular numbers, consider the following pattern:

Put one mark in the middle of a line.

Then, in the line underneath, put 2 marks. You now have three [=t(2)] marks in the form of a triangle.

x

x x

In the next line, put three marks. You now have six [=t(3)] marks in the form of a triangle.

x

x x

x x x

and so on.

Answer 2

There is no such thing as a tiangular number.

A triangular number is a number of the form n*(n+1)/2 for n = 1, 2, 3, ...

It gets its name from the fact that it can be depicted as a triangle as the following, rather crude images show:

x

x

xx

x

xx

xxx

and so on.