Mathematics Class 10
Arithmetic Progressions
Total a stepped list fast, forwards and backwards, from any two facts about it.
14 lessons · ~115 min total
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Lessons in this topic
- 0 Start here A roadmap: the stepped list you can already read, and the total it hides. · 5 min You are here
- 1 Every end pair totals the same Pair the first term with the last on any stepped list. The step cancels, so every end pair totals the same, and Sₙ = n/2 (a + l). · 9 min
- 2 The other face of the sum When the last term is not given, substitute l = a + (n − 1)d into the fold and get Sₙ = n/2 (2a + (n − 1)d) — the same total, a new face. · 9 min
- 3 Working the sum backwards The total is known and n or d is missing: with a and d known (d not 0), solving for n gives a quadratic, solving for d stays linear, and every answer is checked forwards through Sₙ. · 9 min
- 4 Terms from the sums The running total hides the whole list inside it: a₁ = S₁, and every later term is aₙ = Sₙ − Sₙ₋₁ — a rule that looks back from n = 2. · 9 min
- 5 Two sums name the progression A whole progression is just its a and d. Two reported totals give two linear equations about them, and eliminating one letter names the list. · 9 min
- 6 Stacks and rows A real stack earns its total in three moves: read the first term, read the step, and decide whether the question wants one term or all of them. · 9 min
- 7 When the step slides back A step can be negative: a tour riding 3 km less each day is still a real progression, and its total only covers the days the story can hold. · 9 min
- 8 Which question wants the sum Say what a question gives and what it is missing: a term, a total or n. Then check the number you found. · 9 min
- 9 Is it a term of the list? Put a number in the term rule. It is a term if n is whole and at least 1. · 9 min
- 10 Two facts fix the list Two terms give two equations in a and d. Subtract for d, then find a. · 9 min
- 11 Checkpoint: terms, counts and two facts Five quick checks on terms, counting terms and two facts. · 6 min
- 12 The big picture Ten ideas, tied back together. · 6 min
- 13 Track quiz Cheat-sheet table plus a reveal quiz — one question per idea. · 8 min
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