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Extend numerical patterns

Extending numerical patterns means identifying and applying a consistent rule to generate subsequent terms, including patterns involving addition, subtraction, multiplication, division, integers, decimals, and fractions. Learners compare successive terms, distinguish constant differences from constant multiplicative relationships, and represent the rule in a table or simple algebraic expression, recognizing that a pattern must be justified rather than inferred from one coincidence. Formal treatment of arbitrary sequences, complex recursive rules, and advanced general formulas is not included.

Detailed Explanation: Extend numerical patterns

Look at how each term changes to get the next one.

  1. Compare consecutive terms by subtracting:
12−7=5,17−12=5,22−17=5 12-7=5,\qquad 17-12=5,\qquad 22-17=5
  1. Since the difference is always 55, the rule is add 55 each time.

  2. Continue the pattern:

22+5=27,27+5=32,32+5=37 22+5=27,\qquad 27+5=32,\qquad 32+5=37

So the next three terms are:

27, 32, 37\boxed{27,\ 32,\ 37}

A table shows the rule clearly:

Term numberValue
17
212
317
422
527
632
737

The pattern rule can be written as:

next term=current term+5\text{next term}=\text{current term}+5

Always check more than one pair of terms. If the differences are not constant, check whether each term is multiplied or divided by the same number instead.

Learn by doing: Extend numerical patterns

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Patterning - Next in Increasing Arithmetic Number Pattern


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