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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
Look at the pattern: 5, 8, 11, 14. What happens each step? Write a short rule in words.
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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 each pair of neighbors

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

To find the step-by-step pattern, look from one number to the next. Each jump is 3.

02

Notice the repeated change

\[+3,~+3,~+3\]

The same change repeats every time, so this is an additive pattern.

03

Write the rule from one term to the next

\[\text{next}~\text{term}~=~\text{previous}~\text{term}~+~3\]

A recursive-style rule tells how to get each new number from the one before it. Here, you add 3 each time.

04

State the pattern in words

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

This matches all the numbers: starting at 5, adding 3 gives 8, then 11, then 14.

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Another way

  1. Check by rebuilding the pattern: 5, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14.

!

Common mistake

Using 14 - 5 = 9 and saying the rule is add 9. The pattern rule must describe what happens between adjacent terms, not just from the first number to the last.