Page 160 - Maths Class 06

(d) The rule for pattern of letter A is given in the following table:

Number of letters ‘A’ 1 2 3 4 5 … n

Number of matchsticks 6 10 14 18 22 … 4n + 2

Number Patterns

Number patterns can be used to help discovering way to represent certain types of numbers using
variables (literals).
Look at this number series.
1, 5, 9, 13, 17, 21

A careful observation gives us the general formula for the terms as 4n – 3. With the help of this formula,
we can find any term in the number series.
For example,
15th term = 4 × 15 – 3 = 60 – 3 = 57.

35th term = 4 × 35 – 3 = 140 – 3 = 137.
400th term = 4 × 400 – 3 = 1600 – 3 = 1597, and so on.
We can derive some more generalisations, like one given below:

1 × 2 = 2
3 × 2 = 6
5 × 2 = 10
7 × 2 = 14

… … …
From the above, we observe that:

Odd number × 2 = Even number
If n stands for any odd number, 2n represents an even number.

Look at the patterns of squares made by dots.
Thus, nth squares number will be
n × n = n²

4 9 16 25
2 × 2 3 × 3 4 × 4 5 × 5
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