Hint
Subtract each term from the next. Your first two gaps are 4 and 7.
Worked answer
C: 56. The gaps are 4, 7, 10 and 13. Add 3 to the last gap to get 16, then add it to the last term: 40 + 16 = 56. The same gap rule fits all four transitions.
Number sequence practice,
with answers.
Six exercises. Start with a rule family, then test every step. All hints and answers are free.
Each question states a constraint so you can check a specific rule. Try the sequence first, open a hint if you need one, then read the worked answer. These six exercises are separate from the free twelve-question challenge and the printable collection.
No timer or account. You can change your answer and try again. Browser printing uses the questions-only layout by default.
Look between the numbers.
Write down each gap. The gaps can form their own sequence, including when the numbers are falling.
Hint
Keep track of the amount subtracted, rather than only the signed difference.
Worked answer
B: 17. The subtractions are 15, 13, 11 and 9. Each is 2 smaller than the previous subtraction. The next is 7, so 24 − 7 = 17.
Let two operations take turns.
Label the operations above the arrows. Check both parts of the repeating pair before filling the gap.
Hint
The last transition, 34 to 37, used the addition. Which operation has the next turn?
Worked answer
D: 74. Follow ×2, +3, ×2, +3: 7 × 2 = 14; 14 + 3 = 17; 17 × 2 = 34; 34 + 3 = 37. The next operation is ×2, so 37 × 2 = 74.
Hint
Use 2 → 7 to find the addition, then 7 → 21 to find the multiplication. Test the same pair on the remaining terms.
Worked answer
B: 83. The repeating pair is +5, ×3: 2 + 5 = 7; 7 × 3 = 21; 21 + 5 = 26; 26 × 3 = 78. Addition is next, giving 78 + 5 = 83.
Read every other position.
Separate positions 1, 3, 5 from positions 2, 4, 6. A missing seventh term belongs to the odd-positioned sequence.
Hint
Write the odd positions on one line: 3, 7, 11, ?. Put 44, 38, 32 on a separate line.
Worked answer
A: 15. Odd positions increase by 4: 3, 7, 11, 15. Even positions decrease by 6: 44, 38, 32. The gap is in position 7, so continue the first sequence to 15.
Hint
Compare ratios within 5, 10, 20 and within 243, 81, 27, rather than between neighbouring terms.
Worked answer
C: 40. Odd positions double: 5, 10, 20, 40. Even positions divide by 3: 243, 81, 27. The missing seventh term continues the doubling sequence, so it is 40.
Why the constraints matter
A finite list of numbers can fit many formulas. Here, each question names a rule family or operation so the intended answer can be checked against every given term. In a question without a stated constraint, compare plausible simple rules and explain your assumption.
These are recreational learning exercises for adults. They do not provide a standardized IQ score or predict intelligence.
OPTIONAL PRINTABLE COLLECTION
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Reasoning Field Notes contains 24 separate pattern, number and logic exercises, with two hints per exercise and worked solutions. English, Spanish, Brazilian Portuguese and French are included in A4 and US Letter.
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