Page 13 - Ganit Kaushal

6. Observe the following number patterns, which suggest a way of writing the next few terms of a number
sequence.
(i) Find the next three numbers in the sequence: 2, 4, 8, 16, _____, _____, _____ .

Here, the pattern is that – each next term of the sequence is obtained by multiplying two in the
previous term, so the next three terms are 32, 64 and 128. So, the sequence can be written as:
2, 4, 8, 16, 32, 64, 128.
(ii) Find the next three numbers in the sequence: 1, 3, 6, 10, 15, _____, _____, _____ .
Here, the pattern is that – each next term of the sequence is obtained by adding 2, 3, 4, 5, …
respectively to the previous terms. So, the next term of the sequence will be obtained by adding
6, then by adding 7 and then by adding 8. So, the next three terms are 21, 28 and 36 and the
sequence can be written as: 1, 3, 6, 10, 15, 21, 28, 36.

Exercise 1.1

1. Arrange the numbers 16 and 25 as squares.

2. Arrange the numbers 8 and 20 as rectangles.
3. Arrange the number 15 as a triangle.
4. Look at the pattern given below.
7 × 13 = 91

97 × 103 = 9991,
997 × 1003 = 999991,
9997 × 10003 = 99999991, and so on.
Now, complete the following:
(a) 999997 × 1000003 = _____ (b) 9999997 × 10000003 = _____
2
5. Look at the pattern: 1 = 1 × 1 = 1
2
2 = 2 × 2 = 4 = 1 + 3
2
3 = 3 × 3 = 9 = 1 + 3 + 5
Now, complete:
2
2
2
(a) 4 = 4 × 4 = 16 = _____ (b) 5 = 5 × 5 = 25 = _____ (c) 6 = 6 × 6 = 36 = _____
6. Observe the pattern of letters in the sequence given below and choose the correct option to fill in the
blanks.
___ a a d d ___ a d d a ___ d

(a) dad (b) ada (c) dda (d) daa
7. Observe the pattern of letters in the sequence given below and choose the correct option to fill in the
blanks.
a ___ b a ___ b ___ b ___ a ___ b
(a) abaab (b) abbab (c) aabba (d) bbabb
8. Observe the following pattern and fill in the blank.
9 × 3 = 27, 99 × 3 = 297,
999 × 3 = 2997, and so on.

Then 999999 × 3 = _____

Patterns in Mathematics 11