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 The rule is "add 5". The 4th term is 23. What is the 3rd term?
Show worked solution
23 − 5 = 18.
2 The rule is "double". The 3rd term is 40. Give the 2nd and 1st terms.
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40 ÷ 2 = 20; 20 ÷ 2 = 10.
3 The rule is "subtract 7". The 5th term is 12. What is the 4th term?
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12 + 7 = 19.
Level 2 · Core
4 Each term is double the previous plus 3. The 3rd term is 29. What is the 1st term?
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(29 − 3) ÷ 2 = 13; (13 − 3) ÷ 2 = 5. Check: 5 → 13 → 29.
5 Each term is double the previous minus 4. The 4th term is 36. Give the 3rd, 2nd and 1st terms.
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36 → 20 → 12 → 8.
6 Each term is 3 times the previous minus 1. The 3rd term is 23. What is the 1st term?
Show worked solution
(23 + 1) ÷ 3 = 8; (8 + 1) ÷ 3 = 3.
Level 3 · Challenge
7 A sequence starts at 6. Each term is double the previous minus 4.1 The 5th term is 36.
2 The difference between the 4th and 6th terms is 48.
3 The 6th term is 72.
Which statements are correct?
2 The difference between the 4th and 6th terms is 48.
3 The 6th term is 72.
Which statements are correct?
Show worked solution
20 → 36 (1 ✓) → 68. 68 − 20 = 48 (2 ✓). The 6th is 68, not 72 (3 ✗). 1 and 2.
8 A doubling sequence starts at 3: 3, 6, 12, … Give the 4th term, the 6th term, and the difference between them.
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4th 24, 5th 48, 6th 96. 96 − 24 = 72.
9 Each term is double the previous minus 4. The 3rd term is 20. What is the 1st term?
Show worked solution
20 → 12 → 8. Check: 8 → 12 → 20.