Recursive and Direct Pattern Rules

Recursive and Direct Pattern Rules

A recursive rule explains how to get from one term to the next; a direct rule calculates any term from its position. Both are useful. Build a table with term number $n$ and term value, then test a direct rule using more than one row. For linear patterns, the common difference becomes the multiplier of $n$.

Worked example

For $6,10,14,18,\ldots$, the recursive rule is ‘add 4’. A direct rule is $4n+2$: when $n=1$, it gives 6; when $n=4$, it gives 18.

Exam method

1. Find the repeated change. 2. Write a recursive rule. 3. Test a direct rule with the first and another term.