Visual Reasoning in Summation: Area-based Approaches to Arithmetic and Geometric Progressions
Abstract
This classroom note presents two unified, visually motivated derivations for the sums of arithmetic and geometric progressions. Instead of relying solely on algebraic manipulations, each derivation emerges naturally from the areas of bounded regions under simple curves. These area-based proofs offer a pedagogically engaging approach that bridges algebraic reasoning and geometric intuition, helping students visualize classical summation results through the lens of calculus and coordinate geometry.
Keywords: arithmetic progression, geometric progression, visual proof, area under curves
How to Cite:
Rahman, M., (2025) “Visual Reasoning in Summation: Area-based Approaches to Arithmetic and Geometric Progressions”, Ohio Journal of School Mathematics 101(1), 169-171. doi: https://doi.org/10.18061/ojsm.6933
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