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 What is the next term of 9, 13, 17, 21?
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Difference +4, so the next term is 25.
2 What is the common difference of 30, 24, 18, 12?
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24 − 30 = −6. A negative common difference is perfectly valid.
3 Using the rule 2n + 5, what is the 6th term?
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2(6) + 5 = 12 + 5 = 17.
Level 2 · Core
4 Find the rule for 6, 11, 16, 21. (as a rule)
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5n gives 5, 10, 15, 20; each term is 1 more → 5n + 1.
5 Find the rule for 1, 5, 9, 13. (as a rule)
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4n gives 4, 8, 12, 16; each term is 3 less → 4n − 3.
6 Using the rule 3n + 4, what is the 25th term?
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3(25) + 4 = 75 + 4 = 79.
Level 3 · Challenge
7 Is 50 a term of the sequence with rule 4n + 2?
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4n + 2 = 50 → 4n = 48 → n = 12, a whole number → yes, the 12th term.
8 Is 30 a term of the sequence with rule 4n + 1?
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4n = 29 → n = 7.25, not a whole number → no. Positions must be whole and positive.
9 Matchstick triangles in a row use 3, 5, 7, 9 sticks. Find the rule. (as a rule)
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2n gives 2, 4, 6, 8; each is 1 more → 2n + 1. The +1 is the first upright stick; each new triangle adds 2.