Deriving and Applying the Arithmetic Series Sum Formula

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Derive Gauss's formula for the sum of an arithmetic series S_n = n/2(2a_1 + (n-1)d) = n/2(a_1 + a_n) and evaluate finite series.

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Arithmetic Sequences and Series

10th Grade · Math · Open Global Math

6 lessons

Goal

Derive explicit and recursive formulas for arithmetic sequences, calculate partial sums using sigma notation, and model linear progression phenomena.

6 lessons

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Identifying Arithmetic Sequences and the Common DifferenceUp next
Deriving the nth-Term Formula of an Arithmetic SequenceNot started yet
Finding Initial Terms and Differences from Given TermsNot started yet
Deriving and Applying the Arithmetic Series Sum FormulaYou are here
Finding Sums of Arithmetic Series in Sigma NotationNot started yet
Modeling Real-World Situations with Arithmetic Sequences and SeriesNot started yet

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Learning standards covered

OGM.11.NUM.2Open Global Math Standards 2026™ · 10th Grade

Solve problems involving ratios, direct and inverse proportion, compound units (speed, density, pressure), percentage change, financial math (simple/compound interest, annuities, loans, taxation), arithmetic and geometric sequences/series, and nth-term derivations of linear and quadratic sequences.