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

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.