Man vs Maths: L1 Equations of Linear Patterns

Understanding Linear Patterns in Sequences

Introduction to Linear Patterns

• A linear pattern is defined as a sequence where the difference between consecutive terms remains constant. For example, moving from 15 to 18 represents an increase of three, establishing a consistent difference of +3.

Mathematical Representation

• The equation for a linear pattern mirrors that of a line on a graph: y = mx + c. Here, m signifies the gradient (the constant difference), while c denotes the starting point or Y-intercept. This relationship is crucial for understanding linear sequences.

Example of Increasing Sequence

• In an increasing sequence where each term rises by two, the gradient m equals 2. If we trace back to find the zero term, it starts at four, leading to the equation y = 2x + 4. This illustrates how to derive equations from given sequences.

Example of Decreasing Sequence

• Conversely, in a decreasing sequence such as from 41 to 31 (a decrease of -10), the gradient m becomes -10. To find the zero term, one must add ten back from the first term (51), resulting in the equation y = -10n + 51. This demonstrates applying rules consistently across different types of sequences.

General Rule Application