Arithmetic sequences

Math

Definition

A sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference (d). The nth term can be found with a formula, and the sum of the first n terms has a closed-form expression.

Examples

  • 2, 5, 8, 11, 14, ... is arithmetic with common difference d = 3
  • Finding the 50th term of 7, 11, 15, 19, ... → a₅₀ = 7 + (49)(4) = 203
Key Fact

aₙ = a₁ + (n − 1)d; Sum: Sₙ = n/2 · (a₁ + aₙ)

Related Terms

Geometric sequences Sigma notation Linear modeling Function notation

Study This Concept

Practice arithmetic sequences with free review games in these units:

Algebra 2 Unit 8: Sequences and Series