Question

(b) Observe the pattern given below. Identify the constants and the variables, and form a general rule for the number of squares used in the pattern.​

Answer 1

The figures have

1

,

4

,

9

a

n

d

16

squares respectively. The first pattern has

1

square. The second pattern has

4

squares, and so on.

So if we take any figure, the number of squares in the figure will be equal to the square of the number of the figure in order.

If we take the

n

t

h

figure, we have

n

2

squares in that figure.

Hence, the next figure, i.e.,

5

t

h

figure will have

5

2

=

25

squares.

Answer 2

Answer:

Do you what number patterns are? Let us understand this with an example. 1, 4, 7, 10, 13, 16, … What numbers are these? These are the numbers following a certain pattern or sequence. Th number starts with 1 and jumps three numbers every time. Let us study some figures and number patterns in detail.