Visualising Number Sequences
We can learn number patterns using pictures.
Pictures make maths easy and fun to understand 😊
Now, we will see some number patterns with pictures.
Figure it Out
1. Draw the next picture in each sequence
(a) Counting numbers
1, 2, 3, 4, 5 → 6
(b) Odd numbers
1, 3, 5, 7, 9 → 11
(c) Even numbers
2, 4, 6, 8, 10 → 12
(d) Triangular numbers
1, 3, 6, 10, 15 → 21
(e) Square numbers
1, 4, 9, 16, 25 → 36
(f) Cube numbers
1, 8, 27, 64, 125 → 216
2. Why are they called like this?
Triangular Numbers
(1, 3, 6, 10, 15...)
These numbers can be arranged in a triangle shape.
Square Numbers
(1, 4, 9, 16, 25...)
These numbers can be arranged in a square shape.
Cube Numbers
(1, 8, 27, 64, 125...)
These numbers form a cube shape.
3. Number 36
36 can be arranged as:
Triangle
(6 + 5 + 4 + 3 + 2 + 1 + 5 + 4 + 3 + 2 + 1 = 36)
Square
6 × 6 = 36
So, 36 is both a triangular number and a square number.
4. What would you call the following sequence of numbers?
1, 7, 19, 37
These are called Hexagonal Numbers
Pattern of difference:
+6, +12, +18, +24
Next number:
37 + 24 = 61 ✅
5. Visualising Powers of 2 and 3
Powers of 2:
1, 2, 4, 8, 16, 32, 64, ...
👉 Pattern: Each number is multiplied by 2
(1×2 = 2, 2×2 = 4, 4×2 = 8, ...)
Powers of 3:
1, 3, 9, 27, 81, ...
👉 Pattern: Each number is multiplied by 3
(1×3 = 3, 3×3 = 9, 9×3 = 27, ...)
✅ Short Answer:
Powers of 2 → multiply by 2 each time
Powers of 3 → multiply by 3 each time
notebook-style diagrams for this question too 👍
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