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

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

• $n = 4$
• $3 × 4 + 2 = 14$
• So Term 4 is $14$

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 $4$