Lesson 1: Numerical Patterns

Property

Given two numerical patterns, $A$ and $B$, presented in a table, the relationship between their corresponding terms can often be described by an equation. If the difference between corresponding terms is constant, the relationship can be written as $B = A + c$, where $c$ is the constant difference.

Examples

• Consider the table:

The relationship is $B = A + 3$, since each term in Pattern B is 3 more than the corresponding term in Pattern A.

• Consider the table:

The relationship is $Y = X + 4$, since each term in Pattern Y is 4 more than the corresponding term in Pattern X.

Explanation

A table is a useful tool for organizing and comparing two related numerical patterns. By looking at the corresponding terms in each row or column, you can identify a consistent relationship between them. This relationship often involves adding or subtracting a constant value, which is equal to the difference between the starting values of the two patterns.

Property

If two numerical patterns have the same additive rule, the difference between their corresponding terms is constant. This constant difference is equal to the difference between their starting values. For a term at any position $n$, the relationship is:

Examples