Substituting into a Given Rule

Each term in a sequence has a position number

• The first term has position number $1$

• The second term has position number $2$

• The third term has position number $3$

We often use the letter $n$ for the position number

A rule tells us how to find the value of a term

To use the rule, replace $n$ with the position number

For example, use $n = 1$ to find Term 1, $n = 2$ to find Term 2, and $n = 3$ to find Term 3

Sometimes you know the value of a term and need to find its position number

Start with the term value and work backwards

For example, the rule is $3n + 2$ and the term value is $14$

First undo +2: $14 - 2 = 12$

Then undo ×3: $12 ÷ 3 = 4$

So the position number is $4$