Skill: Extend numerical patterns

A numerical pattern follows the same rule each time. To extend it:

1. Compare a term with the term before it.
2. Find the rule, such as “add $6$” or “multiply by $2$.”
3. Use the same rule to find the next terms.
4. Check that the rule works for every pair of terms.

Example: Extend the pattern:

$$6,\ 12,\ 18,\ 24,\ \square,\ \square$$

Compare neighboring terms:

• $6+6=12$
• $12+6=18$
• $18+6=24$

The rule is add $6$ each time.

Continue using the same rule:

• $24+6=30$
• $30+6=36$

So the completed pattern is:

$$6,\ 12,\ 18,\ 24,\ 30,\ 36$$

The pattern continues because every term is found by adding $6$ to the term before it.