S_n = \frac{n}{2} (2a + (n - 1)d)

Sun, 03 May 2026 14:53:54 +0000

# Understanding the Formula for the nth Term of an Arithmetic Sequence: Sₙ = n/2 (2a + (n – 1)d) When studying algebra and sequences, one of the most fundamental and frequently used formulas is the expression for the sum of the first n terms of an arithmetic sequence: Sₙ = n ÷ 2 × (2a + (n – 1)d) This formula enables you to quickly calculate the sum of any arithmetic sequence without adding individual terms one by one. Whether you're a student learning algebra or a teacher explaining key concepts, understanding this formula is essential. In this article, we’ll break down the formula, explore its components, and show how it is applied in mathematical problem-solving.