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The Common Difference

Part of the Expressions & Data section of Coddy's Pre-Algebra journey. Lesson 22 of 51.

A sequence that adds the same number every time is an arithmetic sequence, and that number is its common difference, d. In 4, 10, 16, 22 every gap is 6, so d=10−4d = 10-4, which is 6.

Always subtract in the same direction: a term minus the term before it. In 30, 25, 20, that gives d=25−30d = 25-30, which is -5. The sign carries meaning: a positive d means the sequence grows, a negative d means it shrinks.

Not every sequence is arithmetic. In 1, 3, 9, 27 each term is 3 times the one before, so the gaps are 2, 6 and 18, not equal. Before you name a common difference, check that it really is common to every gap.

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Challenge

7, 11, 15 is the start of an arithmetic sequence. Find its common difference d. Write d as a term minus the term before it, then work it out.

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

quiz iconTest yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Expressions & Data