Page 15 - Ganit Kaushal

The above sequence can be depicted with the help of the following figure, involving red dots being increased
by 1 each time in this pattern. The figure shows the first five terms of the pattern.

1 2 3 4 5 (Counting number pattern)

The counting numbers sequence can also be given by the following formula for its n-th term T as:
n
T = n; n = 1, 2, 3, 4, ……
n
Sequence of Odd Numbers

Consider the sequence 1, 3, 5, 7, 9 …… (Odd numbers)

Can you observe the pattern?
Yes, we can observe that it starts with 1, as 1 is the first odd number, and each next term of the sequence
is obtained by adding 2 to the previous term.
The above sequence can be explained with the help of the following figure, where blue dots are increased by
2 every time in this pattern. The figure shows the first five terms of the pattern.

(Odd number pattern)
1 3 5 7 9
The odd number sequence can also be given by the following formula for its n-th term T as:
n
T = 2n + 1; n = 0, 1, 2, 3, 4 ……
n
Sequence of Even Numbers

Consider the sequence 2, 4, 6, 8, 10 …… (Even numbers)

Can you observe the pattern?
Right! The pattern followed here is that it starts with 2, as 2 is the first even natural number, and each
next term of the sequence is obtained by adding 2 to the previous term.
The above sequence can be explained with the help of the following figure, where green dots are increased by
2 every time in this pattern. The figure shows the first five terms of the pattern.

(Even number pattern)
2 4 6 8 10
The even number sequence can also be given by the following formula for its n-th term T as:
n
T = 2n; n = 1, 2, 3, 4 ……
n
Sequence of Triangular Numbers

A triangular number is a type of number that can be represented by a triangular figure formed by dots. That’s
why they are called triangular numbers. Each triangular number is the sum of the dots forming the triangle.
The triangle must have two equal sides.

These numbers can be visualised by forming a triangle with dots and continuing to expand it.

(Triangular number pattern)
1 3 6 10 15

Patterns in Mathematics 13