Arithmetic Sequences and Explicit Rules

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 10 · Topic 10.1

Arithmetic Sequences and Explicit Rules

An arithmetic sequence adds a constant difference d between consecutive terms.

Definition and explanation

An arithmetic sequence adds a constant difference d between consecutive terms. With first term a₁, its explicit rule is aₙ = a₁ + (n − 1)d for integer n ≥ 1.

Worked example

For 6, 10, 14, 18, the difference is 4. The rule is aₙ = 6 + 4(n − 1), so a₁₀ = 6 + 36 = 42. Substituting n = 1 returns the first term 6.

Common mistake

Using nd instead of (n − 1)d counts one extra step when indexing begins at 1.

Key takeaway

An arithmetic sequence adds a constant difference d between consecutive terms.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.