NCERT Solutions for Class 6th Maths Chapter 1 Patterns in Mathematics
Updated on 2026-09-19
About this chapter
Mathematics is the search for patterns and for the explanations of why those patterns exist. The most basic patterns in mathematics are number sequences — counting numbers, odd, even, triangular, square, cube, Virahānka numbers and powers of 2. Number sequences are often linked in beautiful ways. Adding odd numbers gives squares; adding counting numbers gives triangular numbers; adding hexagonal numbers gives cubes. Drawing a sequence as a picture often explains why a pattern works — a proof you can see. Shape sequences — regular polygons, complete graphs, stacked squares and triangles, the Koch snowflake — are the second big family of patterns, and each is tied to a number sequence.
- What is Mathematics?
- Patterns in Numbers
- Visualising Number Sequences
- Relations among Number Sequences
- Patterns in Shapes
- Relation to Number Sequences
Quick revision
| Sequence | First few terms | How to get the next term | Picture it as |
|---|---|---|---|
| Counting numbers | 1, 2, 3, 4, 5 | +1 | a line of dots |
| Odd numbers | 1, 3, 5, 7, 9 | +2 | bent “L” layers of a square |
| Even numbers | 2, 4, 6, 8, 10 | +2 | two equal rows of dots |
| Triangular | 1, 3, 6, 10, 15 | add the next counting number | a triangle of dots |
| Squares | 1, 4, 9, 16, 25 | add the next odd number | a square grid of dots |
| Cubes | 1, 8, 27, 64, 125 | add the next hexagonal number | a solid cube |
| Hexagonal | 1, 7, 19, 37, 61 | add the next multiple of 6 | rings around a centre dot |
| Virahānka | 1, 2, 3, 5, 8, 13 | add the previous two | spirals and plant growth |
| Powers of 2 | 1, 2, 4, 8, 16 | × 2 | two copies of the last picture |
| Powers of 3 | 1, 3, 9, 27, 81 | × 3 | three copies of the last picture |
Exercises
- Figure it Out — What is Mathematics? Page 2
- Figure it Out — Patterns in Numbers Page 3
- Figure it Out — Visualising Number Sequences Page 5
- In-text Questions — Relations among Number Sequences Page 7
- Figure it Out — Relations among Number Sequences Page 8 & 9
- Figure it Out — Patterns in Shapes Page 11
- Figure it Out — Relation to Number Sequences Page 11 & 12