Page 158 - Maths Class 06

When n = 1, we have:
First term = ´ =3 1 3
Second term = ´ =3 2 6

Seventh term = ´ =3 7 21
and \ 150th term = ´3 150 = 450 and so on.
We can introduce this concept in other figures as well. Let us take a thing say matchsticks and try to
implement this concept in making figures with them.

Patterns from Matchsticks

Let us observe a pattern of letter I (made by three matchsticks) as shown in Fig 11.1. Continue this
pattern with 2 Is and 3 Is and so on.

Fig. 11.1

Prepare a table as given below.

Number of Is formed 1 2 3 4 5 6 7 8

Number of matchsticks required 3 6 9 12 15 18 21 24

If we observe the table we will find that to make one ‘I’ we required thrice the number of matchsticks,. So
we can give a formula for this as,

Number of matchsticks required = ´3 number of Is.
If we put the letter n in place of number of Is, the above formula can be given as :

Number of matchsticks required = ´3 n or 3n
Using this formula we can easily find out the number of NOTE
matchsticks required to form any number of Is. There is no need
to draw a pattern or to make a table for serving this purpose. The word ‘variable’ means something
that can vary, i.e. change.
Here ‘n’ is an example of a variable. Its value is not fixed; it can
take any value 1, 2, 3, 4, 5,….
Let us try another letter say ‘ ’. We can make a pattern of ‘ ’ as under. To make one ‘ ’ we require 5
matchsticks. Study the pattern.

Following table gives us the number of matchsticks required to make a pattern of ’s.

Number of ’s 1 2 3 4 5 6 7 8 9 … … …

Number of matchsticks 5 10 15 20 25 30 35 40 45 … … …

Mathematics-6 158