Introduction
Patterns are sequences that repeat according to a specific rule. In mathematics, number patterns help us understand the relationship between numbers and predict what comes next. Identifying the rule of a pattern is the key to solving number sequences.
Explanation Step by Step
To solve a number pattern, follow these steps:
1. Observe the numbers in the sequence carefully.
2. Check if the numbers are increasing or decreasing.
3. Find the difference between two consecutive numbers.
4. Apply the same rule to find the missing or next number.
A growing pattern where each number increases by 2.Sub-topics
Patterns - Numbers
Number patterns can be based on addition, subtraction, multiplication, or even skip counting. For example, in the sequence 5, 10, 15, 20, the rule is adding 5 to the previous number.
Examples
Example 1
Find the next number in: 10, 20, 30, 40, ...
Observation: Each number is 10 more than the previous one.
Answer: 50
Tricks and Shortcuts
To find a pattern rule quickly, subtract the first number from the second number. If the difference stays the same for the third number, you have found the rule.
Common Mistakes
Assuming a pattern is only about addition. Always check if the numbers are doubling (multiplication) or decreasing (subtraction).
Practice Questions
Easy Questions
- Complete the pattern: 2, 4, 6, 8, __.
- Identify the next number: 11, 22, 33, 44, __.
- What comes next? 5, 10, 15, 20, __.
Medium Questions
- Find the missing number: 100, 90, 80, __, 60.
- Identify the rule and complete: 3, 6, 12, 24, __.
- Complete the sequence: 1, 4, 7, 10, __.
Hard Questions
- Find the next two numbers: 1, 2, 4, 7, 11, __, __.
- What is the 10th number in the pattern: 5, 10, 15, 20...?
- Identify the error in this pattern: 2, 5, 8, 10, 14, 17.
Revision Summary
Patterns follow a fixed rule. By identifying whether a sequence is increasing or decreasing and finding the common difference, we can predict any number in the set.