A growing pattern that adds the same amount at each step can be written as a linear rule: a starting value plus a constant times the term number. Learn to find that rule from a picture pattern, see a worked squares example, and understand why plotting the pattern gives a straight line.
Representing a pattern with a rule
A growing pattern adds the same amount at each step, so it can be described by a linear rule: a starting value plus a constant times the term number.
Worked example
A pattern of squares grows by 3 squares each term: term 1 has 4 squares, term 2 has 7, term 3 has 10, and term 4 has 13. Since each term adds exactly 3, the rule is squares = 3n + 1, where n is the term number.
Plotting the pattern's values against the term number gives a straight line, since the rule is linear.
Notice that plotting term number against the number of squares gives points that fall on a straight line — this is exactly what makes a pattern "linear."
Finding the rule from a pattern
To find the rule for any growing pattern: find the constant difference between consecutive terms (that becomes the coefficient of n), then work out what value makes term 1 come out correctly (that becomes the added constant). This turns a picture or a table of values into an equation you can use to predict any term, and is a first step toward linear equations in general.