Skill: Identify growing patterns

A growing pattern gets bigger by following the same rule each time. To identify the rule:

1. Look at two terms next to each other.
2. Find how much the pattern grows.
3. Check that the same amount is added each time.
4. Use the rule to find the next terms.

Example

A pattern shows the number of tiles in each figure:

Figure	1	2	3	4
Number of tiles	3	6	9	12

Step 1: Compare neighboring terms.

From Figure 1 to Figure 2:

$$6-3=3$$

From Figure 2 to Figure 3:

$$9-6=3$$

From Figure 3 to Figure 4:

$$12-9=3$$

Step 2: Describe the rule.

The number of tiles increases by $3$ each time. The rule is:

Add $3$ to find the next term.

Step 3: Extend the pattern.

Starting with $12$ tiles in Figure 4:

$$12+3=15$$

So Figure 5 has $15$ tiles.

Then:

$$15+3=18$$

So Figure 6 has $18$ tiles.

The extended pattern is:

$$3,\ 6,\ 9,\ 12,\ 15,\ 18$$

Always check that the same amount is added from one term to the next.