Linear Patterns – Extending a Constant-Change Sequence
A linear pattern is a sequence of values in which each term is found by adding (or subtracting) the same fixed amount to the one before it – the pattern version of a linear relationship's constant rate of change. If you plotted each term against its position in the sequence, the points would fall in a perfectly straight line, exactly as they do for any linear relationship.
Once you spot the constant difference in a linear pattern, extending it is simple: just keep adding (or subtracting) that same amount to generate as many further terms as you need.
Extending a Linear Pattern
Find the constant difference between consecutive terms, then add (or subtract) that same amount to extend the pattern.
Each term increases by 5: 19 + 5 = 24.
Differences: 17−20=−3, 13−17=−4, 10−13=−3. Since these are not all equal, this is not a linear pattern.
Real-Life Application
- Seating arrangements: the number of chairs needed as tables are added in a row often forms a linear pattern.
- Staircases: the height gained per step forms a linear pattern.
- Savings goals: a savings balance growing by the same fixed deposit each month is a linear pattern.
Key Takeaways
- A linear pattern changes by the same fixed amount between consecutive terms.
- Extend a linear pattern by repeatedly adding (or subtracting) that constant difference.
- A pattern with an inconsistent difference between terms is not linear.
Practice: Linear Patterns
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