Reasoning

Arithmetic Progression: nth Term

Find any term of an arithmetic progression.

aₙ = a + (n - 1)d

Formula Explanation

Each term increases or decreases by the same common difference.

Variables Explained

aₙ = nth term; a = first term; n = term position; d = common difference.

Solved Example

Find the 10th term when a = 3 and d = 4.
a₁₀ = 3 + (10 - 1) × 4 = 39.

Exam Tip

Use n - 1, not n, when counting the number of differences.