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An arithmetic series sums the terms of an arithmetic sequence using Sₙ = ½n[2a + (n−1)d] or ½n(a + l). This topic covers finding sums, the number of terms and applying series to problems. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
The sum of n terms is n over 2 times twice a plus n minus 1 times d, or n over 2 times the first plus last term when you know both. Choose whichever fits the information given.
Before you start
Best tackled after arithmetic sequences. Pure 2 is where it is assessed. The same ideas return in sum formulae and problem solving.
What you learn
“First to exceed a total” is the same idea as an inequality — find the boundary, then round up. Cumulative amounts (savings, repayments, production) are arithmetic series. The course works through the sum formula, finding n from a sum, sigma notation, A sum and a term together and application: totals and time to reach them. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Arithmetic Series belongs to Sequences & Series and is met in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Nearby topics in the same strand are Binomial Expansion (C12), Binomial Expansion (C34), Geometric Sequences, Geometric Series and Recurrence Relations. For unlimited practice, the Sequences & Series revision engine builds new questions on demand and records your accuracy.
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