Page 16 - Ganit Kaushal

The first few terms of the sequence are 1, 3, 6, 10, 15 …… (Triangular numbers)

Can you observe the pattern?
Well, the pattern followed here is that it starts with 1, and the counting numbers starting with two, i.e.,
2, 3, 4, 5, 6, …. are added respectively each time to get the next term.

Yes, you got it right, the next number in the triangular pattern is 21 because 6 will be added to 15.
The triangular number sequence is also given by the following formula for its n-th term T as:
n
(
nn +1 )
T = ; n = 1, 2, 3…… (The explanation of this formula is beyond the scope of this book.)
n
2
Sequence of Squares
A square number is a type of figurate number that can be represented by a square formed by dots. That’s why
they are called square numbers. Each square number is the sum of the dots forming the square. We know that
a square has all four sides equal.

(Square number pattern)

1 4 9 16 25
The first few terms of the square sequence are 1, 4, 9, 16, 25 …… (Square numbers)
Can you guess the pattern here?

Well, the pattern followed here is ̶ it starts with 1, and the odd numbers starting with three i.e., 3, 5,
7, 9, 11, … are added respectively each time to get the next term.
Yes, you got it right, the next number in the square pattern is 36 because 11 will be added to 25. The sequence
of squares can also be given by the following formula for its n-th term T as:
n
2
T = n ; n = 1, 2, 3, 4 ……
n
Sequence of Cubes

A cubic number is a solid shape type of a number which can be represented by a cube formed by smaller cubes
of side 1 unit. That’s why they are called cubic numbers. Each cube number is the sum of the smaller cubes
(of side 1 unit) forming the bigger cube. We know that the length, breadth and height of a cube are equal.

(Cube number pattern)

1 8 27 64 125

3
3
3
3
3
The first few terms of the cube sequence are 1 , 2 , 3 , 4 , 5 , ……
i.e., 1, 8, 27, 64, 125 …… (Cube numbers)
Can you observe the pattern here?
Well, the pattern followed here is well understood with the help of the given picture. It starts with a
cube of side 1 unit, next is a cube of side 2 units, then a cube with side 3 units, then a cube with side
4 units, then a cube with side 5 units, and so on.
Yes, you got it right, the next term is a cube with a side of 6 units.

14 Mathematics-6