@mathsy.io: Arithmetic Series | Where the Formula Comes From A-Level Maths, Pure — the proof of Sₙ = n/2[2a + (n−1)d], built from the sum written out in full to the formula in the box. What you'll learn: • why the last term is a + (n−1)d, not a + nd — the off-by-one that quietly costs marks • the one move the whole proof turns on: write the entire sum out again, upside down • why every pair across the two lists adds to the same total — whatever you gain at one end, you lose at the other • where the divide-by-2 comes from: you added two whole copies of the sum, and you watch both of them • why there's no condition beside this formula — nothing gets divided by anything that could be zero (unlike the geometric series' r ≠ 1) A step that changes nothing is the hardest kind to think of trying. That's the whole trick. Not in this one: the Sₙ = n/2(a + l) version — same formula, one substitution away, and its own video. #alevelmaths #arithmeticseries #alevelrevision #mathsproof #puremaths

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Sunday 16 August 2026 09:05:00 GMT