What is a pattern?
A pattern is an arrangement of numbers, shapes, or objects that follows a particular rule.
Example:
1. Number pattern: \(2\), \(4\), \(6\), \(8\), \(10\), ....
Rule: Add \(2\) each time.
2. Shape pattern:
Rule: Add \(1\) letter each time.
Pattern helps us predict future terms.
Rule of a pattern(nth term)
To identify a pattern:
- Observe the numbers or shapes carefully.
- Check what changes from one term to the next.
- Write the rule.
Example:
Consider the sequence \(4\), \(8\), \(12\), \(16\), \(20\), ....
Here, we can see that each term in the sequence is a multiple of \(4\).
| Term number | Value in the sequence |
| \(1\) | \(4\) |
| \(2\) | \(8\) |
| \(3\) | \(12\) |
| \(4\) | \(16\) |
| \(5\) | \(20\) |
Therefore, the rule is \(4 \times n\) where \(n\) represents the term number.
Patterns in Calendar
| Sun | Mon | Tue | Wed | Thu | Fri | Sat |
| \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) |
| \(8\) | \(9\) | \(10\) | \(11\) | \(12\) | \(13\) | \(14\) |
| \(15\) | \(16\) | \(17\) | \(18\) | \(19\) | \(20\) | \(21\) |
| \(22\) | \(23\) | \(24\) | \(25\) | \(26\) | \(27\) | \(28\) |
Important observations:
Horizontal pattern of numbers: Add \(1\) to get the next number to the right.
Example: \(16\), \(17\), \(18\)
Vertical pattern of numbers: Add \(7\) to get the number below.
Example: \(5\), \(12\), \(19\), \(26\).
Diagonal pattern of numbers: Add \(8\) each time to get the next number in the diagonal.
Consider the diagonal numbers \(3\), \(11\), \(19\), \(27\).
Here, the difference between each term is \(8\).
Patterns in Matchstick
Matchsticks can form repeating shapes.
Suppose you are given with \(3\) Matchsticks and asking you to form the letter \(C\) using that. Your work might be like this.
Suppose we need \(1\) more \(C\), then we add \(3\) sticks. That is, \(3 + 3 = 6\) sticks.
If totally we need \(3C\)'s, then we need a total stick of \(3 + 3 + 3 = 9\) sticks.
Similarly, if we need \(4C\)'s, then we need \(3 + 3 + 3 + 3 = 12\) matchsticks.
If we need \(6C\)'s, then we need \(3 + 3 + 3 + 3 + 3 + 3 = 18\) matchsticks.
Thus, we get a pattern of \(3\), \(6\), \(9\), \(12\), \(15\), \(18\), ....
We can see that the terms are multiples of \(3\).
Rule for number of matchsticks required \(= 3n\)
Where \(n\) is the number of \(C\)'s in the pattern.