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Mathematics Class 9

Predicting What Comes Next: Exploring Sequences and Progressions

Spot the rule behind a list, name any term, and add n numbers fast.

14 lessons · ~89 min total

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Lessons in this topic

  1. 0 Start here A roadmap: a rule that decides the next number, looking back, jumping straight there, the step, the fold, the multiplier and the tower. · 3 min You are here
  2. 1 A rule, not a guess A list is a sequence with terms. A rule must fit every join, not only the first. · 6 min
  3. 2 A rule that looks back A recursive rule builds each term from the one before. It needs a first term to begin. · 6 min
  4. 3 A rule that jumps straight there An explicit rule gives any term from its position. Solve it to find a number's position. · 6 min
  5. 4 The same step every time An AP adds a fixed difference d. Its nth term is a + (n − 1)d. · 6 min
  6. 5 Adding the first n Two copies of 1 + 2 + … + n fill a rectangle n × (n + 1). One copy is half. · 7 min
  7. 6 Checkpoint: rules, jumps and the fold A graded check on the first five ideas: what a sequence is, looking back, jumping, the nth term, and the fold. · 6 min
  8. 7 The same multiplier every time A GP multiplies by a fixed ratio r. Its nth term is a × r^(n − 1). · 7 min
  9. 8 A shape that multiplies Each stage of a fractal multiplies the count by 3 and the black area by 3/4. · 7 min
  10. 9 A tower and a doubling Moving n discs takes 2 × (moves for n − 1) + 1 moves. That equals 2ⁿ − 1. · 7 min
  11. 10 Does the rule really fit? Two rules can fit the same first terms and part later. A given rule beats a guess. · 7 min
  12. 11 Checkpoint: multipliers, stages, towers and rivals A graded check on the last four ideas: the ratio, the stage offset, the tower cost, and two rules that both fit. · 6 min
  13. 12 The big picture Nine ideas about sequences, tied back to one question: what decides the next number. · 6 min
  14. 13 Track quiz Cheat-sheet table plus a reveal quiz — one question for each of the nine ideas. · 9 min