How to use this practice set
Answer on paper or in your own notes, then open each worked solution. Answers are not collected or saved. There is no time limit. If you want a worksheet, print this page from your browser: questions appear first and the answer key follows on a separate page.
- Describe what changes: quantity, position, direction or symbol. Hold the other features constant while checking one rule.
- Test each transition. If one step breaks your rule, examine alternating operations or separate odd and even positions.
- State the assumed continuation. A finite sequence can fit many rules; these exercises ask for the simple repeated rule described in the solution, not proof of a unique mathematical continuation.
1. Inspect the gaps
Using a rule in which the gap increases by the same amount each time, continue: 3, 7, 13, 21, 31, …
Show answer and explanation: Inspect the gaps
43.
The gaps are 4, 6, 8 and 10. They grow by 2, so the next gap is 12 and 31 + 12 = 43. The terms themselves do not have a constant difference; their differences do.
Check your method: Subtract neighbouring terms first. Adding 10 again would ignore the growth in the gaps.
2. Separate two operations
Continue the repeating two-operation pattern: 4, 7, 14, 17, 34, 37, …
Show answer and explanation: Separate two operations
74.
The operations alternate: add 3, multiply by 2, add 3, multiply by 2, add 3. The next operation is multiply by 2, giving 74. Check the rule from the beginning rather than inferring it from only 34 and 37.
Check your method: Write +3 and ×2 between the numbers. The next operation after 74 would be +3, giving 77.
3. Split odd and even positions
The odd-position terms and even-position terms each follow their own constant-step sequence. Find the missing term: 2, 20, 5, 18, 8, 16, ?, 14.
Show answer and explanation: Split odd and even positions
11.
Odd positions contain 2, 5, 8 and the missing value: add 3 each time. Even positions contain 20, 18, 16 and 14: subtract 2 each time. The missing value belongs to the odd-position sequence, so it is 8 + 3.
Check your method: Number the positions 1 through 8. Treating every adjacent pair as one sequence makes this question unnecessarily complicated.
4. Follow a rotation cycle
An arrow turns by one clockwise quarter-turn each step: up, right, down, left, up, … Which direction follows?
Show answer and explanation: Follow a rotation cycle
Right.
The orientation repeats every four turns. The fifth arrow points up just like the first; the sixth therefore points right just like the second. Counting complete cycles is easier than mentally rotating a long series.
Check your method: A clockwise turn from left points up. If your rule gives down there, you have switched rotation direction.
5. Test the same row rule
In each row, the third value is the sum of the first two. Find the missing value.
Show answer and explanation: Test the same row rule
15.
The rule works in both complete rows: 2 + 5 = 7 and 4 + 6 = 10. Apply the same operation to the last row: 7 + 8 = 15. The prompt gives a row rule, so there is no need to invent a separate column pattern.
Check your method: Validate your operation on every complete row before using it to fill the missing cell.
6. Locate a position in a repeated block
The block circle, square, square, triangle repeats without change. What is the 14th symbol? Count the first circle as position 1.
Show answer and explanation: Locate a position in a repeated block
Square: the second position in the block.
Each block has four symbols. Three complete blocks use positions 1–12. Position 13 starts the next block with a circle, so position 14 is its first square. Equivalently, 14 divided by 4 leaves a remainder of 2.
Check your method: A remainder of zero means the fourth symbol, not a nonexistent position zero. For example, the 12th symbol is a triangle.
Turn an answer into a reusable method
After each question, write the step that made the solution clear. If you missed one, identify whether you misread the instruction, lost track of a position, or applied an inconsistent rule. Retry with that step visible. These six examples are not a calibrated test, and your total cannot establish an IQ, age ranking or population percentile.
Continue practising
- Number sequences: differences, ratios and alternating rules
- Spatial reasoning practice
- Logic puzzles: distinguish a possibility from a necessary conclusion
For a mixed session, try the free reasoning practice test. Read how its estimate works before interpreting the result.
Published by IQTestReal. Editorial policy · Report an unclear question. Include the question title so we can reproduce the issue. This is non-clinical educational practice, not an assessment for admissions, employment or diagnosis.
Answer key: Pattern recognition
1. Inspect the gaps
43. The gaps are 4, 6, 8 and 10. They grow by 2, so the next gap is 12 and 31 + 12 = 43. The terms themselves do not have a constant difference; their differences do.
Check: Subtract neighbouring terms first. Adding 10 again would ignore the growth in the gaps.
2. Separate two operations
74. The operations alternate: add 3, multiply by 2, add 3, multiply by 2, add 3. The next operation is multiply by 2, giving 74. Check the rule from the beginning rather than inferring it from only 34 and 37.
Check: Write +3 and ×2 between the numbers. The next operation after 74 would be +3, giving 77.
3. Split odd and even positions
11. Odd positions contain 2, 5, 8 and the missing value: add 3 each time. Even positions contain 20, 18, 16 and 14: subtract 2 each time. The missing value belongs to the odd-position sequence, so it is 8 + 3.
Check: Number the positions 1 through 8. Treating every adjacent pair as one sequence makes this question unnecessarily complicated.
4. Follow a rotation cycle
Right. The orientation repeats every four turns. The fifth arrow points up just like the first; the sixth therefore points right just like the second. Counting complete cycles is easier than mentally rotating a long series.
Check: A clockwise turn from left points up. If your rule gives down there, you have switched rotation direction.
5. Test the same row rule
15. The rule works in both complete rows: 2 + 5 = 7 and 4 + 6 = 10. Apply the same operation to the last row: 7 + 8 = 15. The prompt gives a row rule, so there is no need to invent a separate column pattern.
Check: Validate your operation on every complete row before using it to fill the missing cell.
6. Locate a position in a repeated block
Square: the second position in the block. Each block has four symbols. Three complete blocks use positions 1–12. Position 13 starts the next block with a circle, so position 14 is its first square. Equivalently, 14 divided by 4 leaves a remainder of 2.
Check: A remainder of zero means the fourth symbol, not a nonexistent position zero. For example, the 12th symbol is a triangle.
Source: https://iqtestreal.com/practice/pattern-recognition. Free non-clinical reasoning practice from IQTestReal.