Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Sequence 5, 10, 20, 40: what comes next?
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Doubling → 80.
2 Machine rule ×4: what comes out when 7 goes in?
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7 × 4 = 28.
3 Pattern ABABAB…: what is the 9th letter?
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Odd positions are A → A.
Level 2 · Core
4 Rule 'double then add 1', start at 3: what is the 4th term?
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3 → 7 → 15 → 31.
5 Machine: 2→9, 3→13, 4→17. What is the rule? (as a rule)
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Out grows 4 per step; 2×4=8, +1 → ×4+1.
6 Pattern: 1 star then 4 moons, repeating. What is the 23rd symbol? (star/moon)
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Block of 5: 23 ÷ 5 = 4 r 3 → 3rd of block = moon.
Level 3 · Challenge
7 Rule 'double minus 3'. A term is 21. What was the term before it?
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Backwards: 21 + 3 = 24, ÷ 2 = 12.
8 Sequence 4, 12, 36, …: difference between the 3rd and 5th terms?
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4th = 108, 5th = 324; 324 − 36 = 288.
9 A pattern repeats 3 red, 2 gold. A bracelet has 18 red beads. How many beads in TOTAL?
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18 ÷ 3 = 6 blocks; each block has 5 beads → 6 × 5 = 30.