Triangular Numbers Pattern

Let us consider the following series of numbers. 1, 3, 6, 10, 15, 21, ….

If we represent each number of above series by a dot and arrange them in such a way that they make a triangle. Such numbers are known as triangular numbers.

Look at the following arrangements of dots.

The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, …

The rule to find the triangular number in a series is:

First term = 1

Second term = First term + 2

Third term = Second term + 3

Fourth term = Third term + 4 and so on.

Examples on Triangular Numbers Pattern:

1. Find the next triangular number in the series 45, 55, …

Solution:

The difference of two terms = 55 – 45 = 10

To get the next term we add 1 more to the previous term difference = 10 + 1 = 11

The next term is 55 + 11 = 66

Questions and Answers on Triangular Numbers Pattern:

I. Given below is a triangular pattern. The dots on each side are same. Draw appropriate number of dots in the empty box to get the next figure of the pattern.

Answer:

II. In the given triangular puzzle, the numbers in the circle add together to make the number in the rectangle. Find the missing numbers in the puzzle.

Answer:

III. Write the next 3 numbers of the triangular series.

1, 3, 6, 10, 15, 21, ……., ……., …….

Answer:

28, 36, 45