NCERT Class 6 Mathematics Textbook for Blind Students made Screen Readable by Professor T K Bansal.

Anita and Sarita are making patterns with matchsticks. They decide to make simple patterns of the letters of the English alphabet. Anita takes two matchsticks and forms the letter L as shown in Figure 11.1 a 

Figure 11.1 a

Then Sarita also, picks two sticks, forms another letter L and puts it next to the one made by Anita [Fig 11.1 b.

Figure 11.1 b

Then Anita adds one more L and this goes on as shown by the dots in Fig 11.1 c.

Figure 11.1 c

Their friend Arjun comes in. He looks at the pattern. Arjun always asks questions. He asks the girls, “How many matchsticks will be required to make seven L’s”? Anita and Sarita are systematic. They go on forming the patterns with one L, two L’s, three L’s, and so on and prepare a table.

Table 1

Arjun gets the answer to his question from the Table 1; 7L’s require 14 matchsticks.

While writing the table, Anita realises that the number of matchsticks required is twice the number of L’s formed.

Number of matchsticks required = 2 × number of L’s.

For convenience, let us write the letter n for the number of L’s.
If one L is made, n = 1;
if two L’s are made, n = 2 and so on;
thus, n can be any natural number 1, 2, 3, 4, 5, .. .. . We then write,

Number of matchsticks required = 2 × n.

Instead of writing 2 × n, we write 2n.

Note that 2n is same as 2 × n.

Anita tells her friends that her rule gives the number of matchsticks required for forming any number of L’s.

Thus, For n = 1, the number of matchsticks required = 2 ×1 = 2.
For n = 2, the number of matchsticks required = 2 ×2 = 4.
For n = 3, the number of matchsticks required = 2 × 3 = 6 etc.

These numbers agree with those from Table 1.

Sarita says, “The rule is very powerful! Using the rule, I can say how many matchsticks are required to form even 100 L’s. I do not need to draw the pattern or make a table, once the rule is known”.

Do you agree with Sarita?