Patterns in Numbers

We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only repeat. Such patterns are known as repeating patterns. A pattern has a group of units that follow a rule while repeating or changing. Let us have a quick review of what we have learnt earlier about patterns.

I. Complete the series by drawing the next figure:

$Complete the Series Patterns$

Answer:

A pattern can also be created with numbers. The set of numbers which follow a common rule form a pattern. For example, the sequence 2, 4, 6, 8, …… can be extended by using the rule of even numbers. Patterns with numbers can also be created using mathematical operations like addition, subtraction, multiplication and division.

For example:

1. Write the next 3 terms of the pattern 11, 15, 19, 23, ……..

The first term is 11. The common difference is 4. The next 3 terms are 27, 31, 35.

Here are some patterns. Follow them and extend them:

(i)

1 × 9 + 2 = 11

12 × 9 + 3 = 111

123 × 9 + 4 = 1111

1234 × 9 + 5 = 11111

12345 × 9 + 6 = _______

123456 × 9 + 7 = _______

(ii)

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = _______

123456 × 8 + 6 = _______

(iii)

111 ÷ 3 = 37

222 ÷ 6 = 37

333 ÷ 9 = 37

444 ÷ 12 = 37

555 ÷ 15 = _______

666 ÷ 18 = _______

(iv)

9 + 1 = 10

90 + 10 = 100

900 + 100 = 1000

9000 + 1000 = _______

90000 + 10000 = _______

900000 + 100000 = _______

Follow the pattern of the following products and extend them further:

(i)

5 × 5 = 25

55 × 5 = 275

555 × 5 = 2775

5555 × 5 = 27775

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

55555555 × 5 = 277777775

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

(ii)

404 × 404 = 163216

505 × 505 = 255025

606 × 606 = 367236

707 × 707 = 499849

808 × 808 = 652864

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _

In patterns in numbers here are some unsolved questions for the students to understand and complete the questions on patterns.

I. Complete the given series:

(i) 1, 3, 5, 7, …….., …….., …….., ……..

(ii) 5, 10, 15, 20, …….., …….., …….., ……..

(iii) 10, 20, 30, 40, …….., …….., …….., ……..

(iv) 3, 5, 8, 12, 17, …….., …….., …….., ……..

(v) 10, 20, 35, 55, 80, …….., …….., …….., ……..

(vi) 2, 2, 3, 3, 3, 4, 4, 4, 4, …….., …….., …….., ……..

(vii) 1, 3, 6, 8, 11, 13, 16, …….., …….., …….., ……..

(viii) 35, 45, …….., 65, 75, …….., 95

(ix) 100, 90, 80, …….., 60, 50 ……..

(x) 1, 3, 5, 7, 9, …….., …….., …….., ……..

Answer:

I. (i) 9, 11, 13, 15

(ii) 25, 30, 35, 40

(iii) 50, 60, 70, 80

(iv) 23, 30, 38, 47

(v) 110, 145, 185, 230

(vi) 5, 5, 5, 5, 5

(vii) 18, 21, 23, 26

(viii) 55, 85

(ix) 70, 40

(x) 11, 13, 15, 17

II. Complete the series:

(i) 1, 4, 7, 10, 13, 16, …….., …….., …….., ……..

(ii) 12, 17, 22, 27, 32, …….., …….., …….., ……..

(iii) 6, 16, 26, 36, 46, …….., …….., …….., ……..

(iv) 10, 30, 50, 70, …….., …….., …….., ……..

(v) 38, 35, 32, 29, …….., …….., …….., ……..

(vi) 54, 50, 46, 42, …….., …….., …….., ……..

(vii) 53, 49, 45, 41, …….., …….., …….., ……..

(viii) 23, 30, 37, 44, …….., …….., …….., ……..

Answer:

II. (i) 19, 22, 25, 28

(ii) 137, 42, 47, 52

(iii) 56, 66, 76, 86

(iv) 90, 110, 130, 150

(v) 26, 23, 20, 17

(vi) 38, 34, 30, 26

(vii) 37, 33, 29, 25

(viii) 51, 58, 65, 72

III. Complete the following series:

(i) 7, 14, 21, 28, …….., …….., …….., ……..

(ii) 25, …….., 75, 100, …….., …….., …….., ……..

(iii) 10, 100, …….., 10000, 100000, ……..

(iv) 2, 10, …….., 250, 1250

(v) 500000, 50000, …….., 500, …….., 5

(vi) 64, 32, 16, …….., 4, …….., 1

(vii) 5, 10, 20, …….., 80, …….., 320

(viii) 8, 16, 24, 32, …….., …….., …….., ……..

(ix) 45, 54, 63, …….., …….., …….., ……..

(x) 2, 6, 18, 54, ……..

Answers:

III. (i) 7, 14, 21, 28, …….., …….., …….., ……..

(ii) 25, …….., 75, 100, …….., …….., …….., ……..

(iii) 10, 100, …….., 10000, 100000, ……..

(iv) 2, 10, …….., 250, 1250

(v) 500000, 50000, …….., 500, …….., 5

(vi) 64, 32, 16, …….., 4, …….., 1

(vii) 5, 10, 20, …….., 80, …….., 320

(viii) 8, 16, 24, 32, …….., …….., …….., ……..

(ix) 45, 54, 63, …….., …….., …….., ……..

(x) 2, 6, 18, 54, ……..

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