Patterns In | Class 6 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 min read
Patterns In – this guide gives you a concise, exam-ready overview of Patterns In from Class 6 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
1.2 Patterns in Numbers
One of the most fundamental types of patterns in mathematics is found in numbers, especially whole numbers (0, 1, 2, 3, 4, ...). The branch of mathematics that studies these patterns is called number theory. Number sequences, which are ordered lists of numbers following a particular rule, are among the simplest and most fascinating patterns.
Table 1 in the textbook lists several important number sequences:
- All 1's: 1, 1, 1, 1, 1, ...
- Counting numbers: 1, 2, 3, 4, 5, 6, 7, ...
- Odd numbers: 1, 3, 5, 7, 9, 11, 13, ...
- Even numbers: 2, 4, 6, 8, 10, 12, 14, ...
- Triangular numbers: 1, 3, 6, 10, 15, 21, 28, ...
- Squares: 1, 4, 9, 16, 25, 36, 49, ...
- Cubes: 1, 8, 27, 64, 125, 216, ...
- Virahānka numbers (Fibonacci sequence): 1, 2, 3, 5, 8, 13, 21, ...
- Powers of 2: 1, 2, 4, 8, 16, 32, 64, ...
- Powers of 3: 1, 3, 9, 27, 81, 243, 729, ...
Each sequence follows a specific rule for generating the next term. For example, the counting numbers increase by 1 each time, odd numbers increase by 2, and powers of 2 multiply the previous term by 2.
Recognizing these patterns helps develop mathematical thinking and problem-solving skills.
📊 Diagram: Table 1 lists number sequences with examples of their terms.
🧪 Activity: Figure it Out: Students are encouraged to recognize the pattern in each sequence, write the next three numbers, and describe the rule in their own words.
🔗 Connection: Leads to visualizing these number sequences using pictures and diagrams in the next section.
Frequently asked questions
Q.2. Why are 1, 3, 6, 10, 15, ... called triangular numbers? Why are 1, 4, 9, 16, 25, ... called square numbers or squares? Why are 1, 8, 27, 64, 125, ... called cubes?
These sequences are named based on the shapes formed by arranging dots:
- Triangular numbers (1, 3, 6, 10, 15, ...) represent dots arranged in an equilateral triangle.
- Square numbers (1, 4, 9, 16, 25, ...) represent dots arranged in a perfect square.
- Cube numbers (1, 8, 27, 64, 125, ...) represent dots arranged in a perfect cube.
Refer to Table 2 on page 4 for pictorial illustrations.
Q.3. You will have noticed that 36 is both a triangular number and a square number! That is, 36 dots can be arranged perfectly both in a triangle and in a square. Make pictures in your notebook illustrating this!
36 is a triangular number because it can be arranged as a triangle with 8 rows (sum of first 8 natural numbers = 36). It is also a square number because 6 × 6 = 36, so dots can be arranged in a 6 by 6 square. Draw these arrangements in your notebook to visualize.
Q.4. What would you call the following sequence of numbers?
The answer given is 61. (Note: The original question seems incomplete or missing the sequence itself in the text.)
Q.5. Can you think of pictorial ways to visualise the sequence of powers of 2? powers of 3?
For powers of 2, refer to the sequence given on page 6. For powers of 3, one way is to visualize cubes growing in size, as shown in the images (img-12.jpeg to img-15.jpeg) illustrating the cubes of 1, 3, 9, 27, etc.
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