Sunday, August 23, 2009

Number Pattern - Triangular Numbers

Let the numbers be represented with square boxes.
i.e 1 with one square box, 2 with two square boxes, 3 with 3 square boxes and so on.
Arrange the square boxes representing a number in the form of a triangle.
The numbers for which we can make such an arrangement are called Triangular numbers.

The first triangular number is 1.
The second triangular number is 3, which is 1+2.
The third triangular number is 6, which is 1+2+3.
The fourth triangular number is 10, which is 1+2+3+4.
Continuing this pattern, the fifth triangular number is the sum of first five natural numbers.
The nth triangular number is the sum of the first n natural numbers.

It is not possible to arrange the square boxes

representing the numbers 2,4,5,7,8,9,... in the form of a triangle.

So they are not triangular numbers.

See the Pattern..

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1 + 2 + 3 + 4 + 5 = 15

1 + 2 + 3 + 4 + 5 + 6 = 21

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

1 comment:

  1. The informatio u provided is great and helpful. Can u illustrate it through some more examples

    ReplyDelete