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Predicting What Comes Next: Exploring Sequences and Progressions

Checkpoint: multipliers, stages, towers and rivals

Four lessons since the last checkpoint. Take the set again as often as you like.

A GP starts at 2 and multiplies by 3 each step. What is its term at position 5?

A list starts at 48 and multiplies by 1/2 each step. What is it?

How many black triangles does stage 4 of the Sierpiński triangle have?

The tower needs 1 move for 1 disc. It doubles, plus one, at each size. How many moves for 5 discs?

The list 3, 5, 7 fits "add 2 each time". It also fits "the odd primes". What follows?

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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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