Extend numerical patterns

A numerical pattern is an ordered sequence in which each term is related to the preceding term by a consistent rule, such as adding, subtracting, multiplying, or dividing by a whole number. Learners determine the rule from given terms and use it to extend sequences, fill missing terms, and explain why the pattern continues, using tables or number lines when helpful; formal algebraic formulas, arbitrary sequences, and generalized nth-term rules are beyond this scope.

Detailed Explanation: Extend numerical patterns

A numerical pattern follows the same rule each time. To extend it:

Compare a term with the term before it.
Find the rule, such as “add $6$ ” or “multiply by $2$ .”
Use the same rule to find the next terms.
Check that the rule works for every pair of terms.

Example: Extend the pattern:

6,\ 12,\ 18,\ 24,\ \square,\ \square

Compare neighboring terms:

$6+6=12$
$12+6=18$
$18+6=24$

The rule is add $6$ each time.

Continue using the same rule:

$24+6=30$
$30+6=36$

So the completed pattern is:

6,\ 12,\ 18,\ 24,\ 30,\ 36

The pattern continues because every term is found by adding $6$ to the term before it.

Learn by doing: Extend numerical patterns

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Patterning - Next in 4 Item Repeating Number Pattern

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Extend numerical patterns

Detailed Explanation: Extend numerical patterns

Learn by doing: Extend numerical patterns

Practice with unlimited practice problems

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Patterning - Next in 4 Item Repeating Number Pattern