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Triangular Number

A triangular number (triangle number) is a number that represents the pattern of dots arranged in a way that they form an equilateral triangle. An equilateral triangle (also known as a regular triangle) is the one in which all the three sides are of equal length.

A triangular number is denoted by Tn that represents the number of dots.

Mathematical Formula

Below is the mathematical formula for a triangular number:

where n is a positive number such as 1, 2, 3, 4, 5, ..... , n.

Triangular Number Sequence

Below is the triangular number sequence:

[1, 3, 6, 10, 15, 21, 28, 36, ..... ]


Example

For n = 1

Putting this value of n in the above mathematical formula:

T1 = 1(1 + 1)/2

T1 = 1(2)/2

T1 = 2/2

T1 = 1

For n = 2

Putting this value of n in the above mathematical formula:

T2 = 2(2 + 1)/2

T2 = 2(3)/2

T2 = 6/2

T2 = 3

For n = 3

Putting this value of n in the above mathematical formula:

T3 = 3(3 + 1)/2

T3 = 3(4)/2

T3 = 12/2

T3 = 6

For n = 4

Putting this value of n in the above mathematical formula:

T4 = 4(4 + 1)/2

T4 = 4(5)/2

T4 = 20/2

T4 =10

Hope you have understood this amazing concept of triangular number. You can try yourself using other values of n. In case of any issue, provide your valuable comments.

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