Numbers and sequences
Square & triangular numbers
Square numbers and triangular numbers are two special sequences you can see as patterns of dots.
The two patterns
ā¢ Square numbers come from a number multiplied by itself: 1, 4, 9, 16, 25, ā¦ (up to 100). ā¢ Triangular numbers add one more each step: 1, 3, 6, 10, 15, ā¦ (they make a triangle of dots).
Worked examples
A square number
- Find the 5th square number.
- Multiply the position by itself: 5 Ć 5.
Answer: The 5th square number is 25.
A triangular number
- The triangular numbers are 1, 3, 6, 10, ā¦
- The gaps grow: +2, +3, +4, +5. So add 5 to 10.
Answer: The next triangular number is 15.
Where you see this in real life
- Arranging tiles or stamps in a perfect square.
- Stacking cans or oranges in a triangle.
- Spotting square patterns in windows or tiled floors.
Key words
- Square number
- The result of multiplying a whole number by itself, e.g. 9 = 3 Ć 3.
- Triangular number
- A number of dots that can be arranged as a triangle: 1, 3, 6, 10, ā¦
- Sequence
- A list of numbers that follow a rule.