Number Patterns & Rules

A number pattern (or sequence) follows a rule. Two common kinds:

• Constant difference: each term is the previous one plus (or minus) a fixed number. In $3, 7, 11, 15, \dots$ the rule is "add $4$", so the next term is $19$.
• Constant ratio: each term is the previous one times a fixed number. In $2, 4, 8, 16, \dots$ the rule is "multiply by $2$", so the next term is $32$.

A position rule links each term to its position number. For $4, 7, 10, 13, \dots$ the rule is "multiply the position by $3$, then add $1$": position $1$ gives $3 + 1 = 4$, position $2$ gives $6 + 1 = 7$, and so on. That lets you jump straight to, say, the $10$th term.