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.
Look at how each term changes to get the next one.
Since the difference is always , the rule is add each time.
Continue the pattern:
So the next three terms are:
A table shows the rule clearly:
| Term number | Value |
|---|---|
| 1 | 7 |
| 2 | 12 |
| 3 | 17 |
| 4 | 22 |
| 5 | 27 |
| 6 | 32 |
| 7 | 37 |
The pattern rule can be written as:
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.
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