The Common Difference
Part of the Expressions & Data section of Coddy's Pre-Algebra journey. Lesson 23 of 52.
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 - 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 - 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.
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.
This lesson includes a short quiz. Start the lesson to answer it and track your progress.
This lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Expressions & Data
1Variables and Expressions
What a Variable IsWriting ExpressionsExpressions from StoriesTwo OperationsRecap: Expressions2Evaluating Expressions
Substituting a ValueNegative InputsPowers in ExpressionsFormulasRecap: Evaluating5Patterns and Sequences
Continuing a PatternThe Common DifferenceThe nth TermWriting the RuleRecap: Sequences3The Distributive Property
Number PropertiesMental MathDistributing LettersDistributing a MinusRecap: Distributing