Checkpoint: multipliers, stages, towers and rivals

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

• 2 + 3 + 3 + 3 + 3 = 14
• 2 × 3⁴ = 162
• 2 × 3⁵ = 486

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

• Not a GP, because a GP must grow
• An AP with a negative step
• A GP that shrinks

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

• 81, from 3⁴
• 12, from 3 × 4
• 64, from 4³

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

• 5, one move per disc
• 31, from 15 doubled, plus 1
• 32, from doubling five times

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

• Neither wins. Three terms cannot choose
• The primes win, because they explain the numbers
• "Add 2" wins, because it is simpler