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Predicting What Comes Next: Exploring Sequences and Progressions

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5, 8, 11 sit on a board. What comes after 11?

One rule, checked twice, names the next number.

This track follows Chapter 8 of Ganita Manjari (Class 9, Part I). Its name is Predicting What Comes Next: Exploring Sequences and Progressions.

What you will learn

  • A rule, not a guess — a rule must fit every join. A join is where two terms meet.
  • Looking back — building each term from the one before it.
  • Jumping straight there — finding any term with one working.
  • The same step every time — the arithmetic progression and its nth term.
  • Adding the first n — pairing a list to add it fast.
  • The same multiplier every time — the geometric progression.
  • A shape that multiplies — counting triangles in a fractal, stage by stage.
  • A tower and a doubling — a puzzle whose moves double, plus one.
  • Does the rule really fit? — why three numbers cannot settle a rule.

Need a quick recap?

Five earlier lessons help here. You can start this track without them.

  • The case that breaks it — one wrong case can sink any claim.
  • From five examples to every number — turning lucky guesses into proof.
  • A short way to write repeated multiplying — the raised number counts them.
  • A shape inside itself — one rule, run again at a smaller size.
  • What each stage really does — count a repeated rule's output for real.

Jump to lesson

This track

  1. 0 Start here
  2. 1 A rule, not a guess
  3. 2 A rule that looks back
  4. 3 A rule that jumps straight there
  5. 4 The same step every time
  6. 5 Adding the first n
  7. 6 Checkpoint: rules, jumps and the fold
  8. 7 The same multiplier every time
  9. 8 A shape that multiplies
  10. 9 A tower and a doubling
  11. 10 Does the rule really fit?
  12. 11 Checkpoint: multipliers, stages, towers and rivals
  13. 12 The big picture
  14. 13 Track quiz

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