Patterns in Numbers

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.2

Learn

The most basic patterns are patterns in whole numbers: 0, 1, 2, 3, 4 … The part of maths that studies them is called number theory. A list of numbers made by a rule is a number sequence.

Some simple sequences: all 1's (1, 1, 1 …), counting numbers (add 1 each time), odd numbers (start at 1, add 2) and even numbers (start at 2, add 2).

Even: 2, 4, 6, 8, 10 …

Triangular numbers: 1, 3, 6, 10, 15 … Look at the jumps: +2, +3, +4, +5. The jump grows by one each time.

Square numbers: 1 × 1, 2 × 2, 3 × 3 … that is 1, 4, 9, 16 … Their jumps are 3, 5, 7, 9: the odd numbers! Cube numbers: 1 × 1 × 1, 2 × 2 × 2 … that is 1, 8, 27, 64. They grow very fast.

Cubes: 1, 8, 27, 64, 125 …

Virahānka numbers: 1, 2, 3, 5, 8, 13 … Each number is the sum of the two before it (5 + 8 = 13). The Indian scholar Virahānka found them more than 1000 years ago while studying rhythms in poetry.

5 + 8 = 13

Powers of 2: start at 1 and double each time: 1, 2, 4, 8, 16 … Powers of 3: multiply by 3 each time: 1, 3, 9, 27, 81 …

Powers of 3: 1, 3, 9, 27, 81 …

Explore: make your own number patterns. Choose where to start and how much to add each time.

1. Make the odd numbers: 1, 3, 5, 7 …
2. Make the multiples of 5: 5, 10, 15 …
3. Make a pattern in which 4, 10 and 22 all appear.

Remember

• A number sequence is a list of numbers made by a rule.
• Odd 1, 3, 5 … · Even 2, 4, 6 … · Triangular 1, 3, 6, 10 … · Squares 1, 4, 9, 16 … · Cubes 1, 8, 27 … · Virahānka 1, 2, 3, 5, 8 … · Powers of 2: 1, 2, 4, 8 …

Quick check

Which number comes next? 1, 2, 3, 5, 8, 13, …

1. 18
2. 20
3. 21
4. 26

Think about it

Write the next three numbers of each sequence, and say its rule in your own words.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.