How to Use Summation Formulas for Arithmetic and Geometric Series Definition, Types, Examples & Uses

How to Use Summation Formulas for Arithmetic and Geometric Series

Subject: Mathematics

Book: Maths Mastery

Arithmetic series Sₙ= (n/2)(a₁+aₙ) or (n/2)[2a₁+(n–1)d] sums n terms. Geometric series Sₙ= a₁(1–rⁿ)/(1–r) for r≠1. These standard results handle repeated adding or multiplying patterns. For example, if an arithmetic sequence is 5, 8, 11,... with n=6 terms, sum is (6/2)[2×5+(6–1)×3]=3[10+15]=75. Mastery helps with finances (loan amortization), repeated additions in budgeting, or analyzing growth in discrete steps. Summation formulas are cornerstones of advanced math, bridging simple patterns to deep combinatorial or calculus expansions.