Question

Write a note on triangular and square numbers.

Answer 1

Note on triangular and square numbers :

The representation of numbers in the form of an equilateral triangle arranged in a sequence is known as the triangular number sequence.

For example:

• First number is $1$
• In number $2,$ a row is added with two dots to the first number
• In number $3$, a row is added with three dots to the second number
• Again, in number $4$, a row is added with four dots to the third number and so on

If each number in a series$1,4,9,16,25,\dots$ can be represent by a dot in such a way that they make a square. Such numbers are known as square numbers.

Square numbers can be obtained by squaring a number.

First term ,$1^2=1$

Second term, $2^2=4$

Third term, $3^2=9$

Fourth term ,$4^2=16$

Thus, in the pattern of triangular numbers, the next number is obtained in the sequence by adding the previous row , and square numbers can be obtained by squaring.