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All courses Math Foundations · MF.GR.2 41 of 60
Identify a numerical pattern and write a rule that matches it.

Describe how a pattern changes each step

Problem
Analyze the pattern \(5,~8,~11,~14\) and state a short rule in words for the change at each step.
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Hint

Look at each pair of neighboring numbers: from 5 to 8, from 8 to 11, and from 11 to 14. Find how much the pattern changes each time.

For a step-by-step pattern, compare one term to the next. If the same change repeats, describe that repeated change in words.

Solution walkthrough

01

Compare neighboring terms

\[8~-~5~=~3;~11~-~8~=~3;~14~-~11~=~3\]

A step-by-step rule must describe the change from each term to the next, so compute all three adjacent differences.

02

Identify the repeated change

\[5~\to~8~\to~11~\to~14:~+3~\text{each}~\text{step}\]

Every adjacent difference is positive three, so the same addition generates every listed term after the first.

03

Check the rule

\[5~+~3~=~8;~8~+~3~=~11;~11~+~3~=~14\]

Applying the proposed rule reproduces the complete sequence, not just one pair of terms.

04

State the rule in words

\[\text{Add}~3~\text{each}~\text{step}.\]

The pattern increases by three whenever it advances one position.

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Another way

  1. Draw equal arrows between consecutive terms and label each arrow plus three.

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Common mistake

Do not subtract the first term from the last and call that the step size; the step size comes from neighboring terms.

Solution walkthrough video