Checkpoint: rules, jumps and the fold

A list is 2, 5, 9, 14. The gaps are 3, 4, 5. What follows?

• The rule is "add 3", because the first gap is 3
• No single add or multiply rule fits every join
• The rule is "rise every step"

t₁ = 4 and tₙ = tₙ₋₁ + 5. What is t₄?

• 14, from 4 + 2 × 5
• 19, built as 4, 9, 14, 19
• 24, from 4 + 4 × 5

A list has the rule tₙ = 3n + 2. Is 138 a term?

• Yes, because 3 × 46 = 138
• Yes, because 138 is more than 5
• No, because 3n + 2 = 138 gives n = 45.33

An AP starts at 7 and adds 6 every step. What is its 20th term?

• 127, from 7 + 20 × 6
• 121, from 7 + 19 × 6
• 120, from 6 × 20

What is 1 + 2 + 3 + … + 20?

• 420, from 20 × 21
• 210, from 20 × 21 ÷ 2
• 200, from 20 × 10