Patterns in Mathematics | Mathematics Grade 6 CBSE

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Six kinds of pattern

A pattern is any arrangement that follows a rule. Tap each term to see how it is built, the rule behind it, and where it shows up.

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The three big ideas

A sequence is a list of numbers in order, built by a rule. The numbers are called terms.
Counting numbers: 1, 2, 3, 4 … (add 1). Even: 2, 4, 6, 8 … (add 2). Odd: 1, 3, 5, 7 … (add 2, starting at 1).
Doubling gives the powers of two: 1, 2, 4, 8, 16, 32 … (multiply by 2 each time).
Virahānka (Fibonacci) numbers: 1, 1, 2, 3, 5, 8, 13 … each term is the sum of the two before it.

Common mistake: assuming every sequence grows by adding the same amount. Always test your rule on three or four terms before trusting it – doubling and Virahānka sequences grow by different amounts each step.

Square numbers 1, 4, 9, 16, 25 come from arranging dots in squares: 1×1, 2×2, 3×3 … The nth square number is n × n = n².
Triangular numbers 1, 3, 6, 10, 15 come from stacking dots in triangles: the nth one is 1 + 2 + 3 + … + n.
Hidden link: adding consecutive odd numbers always makes a square number – 1 = 1, 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16.
Regular shapes also form a sequence: triangle (3 sides), square (4), pentagon (5), hexagon (6) – each adds one side.

Worked example. Show that the 5th triangular number equals 15, then find the 6th.

Step 1. The nth triangular number is 1 + 2 + 3 + … + n.

Step 2. 5th term = 1 + 2 + 3 + 4 + 5 = 15. ✓

Step 3. The 6th term just adds the next counting number: 15 + 6 = 21.

To continue a pattern, find the rule first. Look at the gap between terms: is it the same each time (add), is it multiplying (double), or does it depend on earlier terms?
Once you have the rule, you can predict any term – even far ahead – without writing all the ones in between.
Patterns in nature: many flowers have a Virahānka number of petals; sunflower seeds and pinecones spiral in those same numbers; snowflakes show six-fold symmetry; honeycombs are tiled with hexagons.

Worked example. What comes next in 1, 4, 9, 16, ___ ? And what is the 10th term?

Step 1. Test a rule: 1 = 1², 4 = 2², 9 = 3², 16 = 4². These are the square numbers.

Step 2. Next term is 5² = 25.

Step 3. The 10th term is 10 × 10 = 100 – found straight from the rule, no need to list the others.

Common mistake: guessing the next term from just one gap. Check your rule against at least three terms – the sequence 1, 2, 4 could be "add 1 then 2" or "double", so you need more terms to be sure.

Where you'll meet it

Patterns at work

Rangoli & kolam designs

Festival rangoli and South-Indian kolam are built on grids of dots joined by repeating, symmetric rules. Knowing how the pattern grows lets you scale a small design up to fill a whole doorway without losing its balance.

Calendars & timetables

The same weekday repeats every 7 days, festivals fall on predictable cycles, and bus arrivals follow a fixed gap. Spotting the period of a repeating pattern tells you when an event happens next.

Predicting & saving

If you save ₹5 in week 1, ₹10 in week 2, ₹15 in week 3 … the rule "add ₹5" lets you say exactly how much you'll have in week 20 – useful for planning a goal long before you get there.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and case studies, testing whether you can use the ideas, not just recall them.

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