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Algebra

Arithmetic Sequence

Formula
aₙ = a₁ + (n − 1)d

What is Arithmetic Sequence?

An arithmetic sequence is a sequence where each term increases by a constant difference d. The nth term is found by adding the common difference (n−1) times to the first term.

Variables

  • a
    aₙ — nth term
  • a
    a₁ — First term
  • n
    n — Term number
  • d
    d — Common difference

Worked Examples

Example 1

Find the 10th term of the sequence 3, 7, 11, 15, ...

Solution:

a₁ = 3, d = 4. a₁₀ = 3 + (10−1) × 4 = 3 + 36 = 39

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