Identify repeating patterns

Repeating patterns are sequences of numbers, shapes, symbols, or other elements in which a fixed block of terms—the repeat unit—recurs in the same order. Learners identify the shortest repeat unit and use its position to determine missing or later terms across representations, distinguishing repetition from a pattern that grows by addition or another rule; formal sequence notation and generalized periodic-function analysis are not included.

Detailed Explanation: Identify repeating patterns

A repeating pattern has a repeat unit: the shortest group of terms that keeps appearing in the same order.

Example

What are the next four symbols, and what symbol is in position $(14)$ ?

\star,\ \circ,\ \circ,\ \triangle,\ \star,\ \circ,\ \circ,\ \triangle,\ \star,\ \circ,\ \circ,\ \triangle,\ \_\_,\ \_\_,\ \_\_,\ \_\_

Step 1: Find the shortest group that repeats.

Group the symbols:

\underbrace{\star,\ \circ,\ \circ,\ \triangle}_{\text{repeat unit}} \quad \underbrace{\star,\ \circ,\ \circ,\ \triangle}_{\text{repeat unit}} \quad \underbrace{\star,\ \circ,\ \circ,\ \triangle}_{\text{repeat unit}}

The repeat unit is:

\star,\ \circ,\ \circ,\ \triangle

It has $4$ symbols.

Step 2: Continue the repeat unit.

After the third group, start the same unit again:

\star,\ \circ,\ \circ,\ \triangle

So positions $(13)$ through $(16)$ are:

\star,\ \circ,\ \circ,\ \triangle

Step 3: Find position $(14)$ .

Position $(14)$ is the second symbol in the new group. The second symbol is $\circ$ .

Answer:

The next four symbols are $\star,\ \circ,\ \circ,\ \triangle$ .
The symbol in position $(14)$ is $\circ$ .

Remember: a repeating pattern uses the same group again and again. A pattern such as $(2,4,6,8)$ grows by adding $2$ , so it is not a repeating pattern.

Learn by doing: Identify repeating patterns

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Patterning - Next in 3 Item Repeating Number Pattern

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