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
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