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Extend repeating patterns

Extending a repeating pattern involves identifying its smallest repeating unit and preserving the unit’s order to determine missing or subsequent elements in numerical, symbolic, or visual patterns. The reasoning distinguishes a true cycle from a growing pattern and recognizes that an element’s position within the cycle determines what repeats, rather than simply continuing the most recent change. General formulas for arbitrary terms and more advanced periodic functions are not included.

Detailed Explanation: Extend repeating patterns

A repeating pattern is a pattern that goes through the same group of items again and again. The smallest group that repeats is called the repeating unit.

To extend a pattern:

  1. Look for the smallest group that repeats.
  2. Check that the group appears again in the same order.
  3. Continue that order to find the next items.

Example: Find the next four numbers:

4, 7, 9, 4, 7, 9, __, __, __, __4,\ 7,\ 9,\ 4,\ 7,\ 9,\ \_\_,\ \_\_,\ \_\_,\ \_\_

Step 1: Find the repeating unit.

The numbers 4,7,94, 7, 9 repeat:

4, 7, 9∣4, 7, 9∣⋯4,\ 7,\ 9 \mid 4,\ 7,\ 9 \mid \cdots

So the repeating unit is:

4, 7, 94,\ 7,\ 9

Step 2: Continue the unit in the same order.

After the second 99, the unit starts again with 44, then 77, then 99, then 44.

Answer:

4, 7, 9, 4, 7, 9, 4, 7, 9, 44,\ 7,\ 9,\ 4,\ 7,\ 9,\ \boxed{4,\ 7,\ 9,\ 4}

Do not just continue the most recent change. The pattern is not growing; it is repeating the same unit 4,7,94, 7, 9 again and again.

Learn by doing: Extend repeating patterns

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    Patterning - Term Value for 4 Item Repeating Shape Pattern

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