Series (Number & Letter)
🔒 Log in to trackWrong number in the series
🔒 Log in to trackIn a wrong-number question the series is already complete, but one term does not fit. You must name that term as it is shown, not the correct value. The wrong term sits between two gaps that look wrong.
What the question asks
The series is complete, but one term was changed. Find that wrong term. Do not give the correct value.
Think of a bank passbook with one typing error. Every other entry follows the rule. Only one entry breaks it.
The basic method
- Take the first three or four terms and guess the rule.
- Test the guess on every term, one by one.
- The term that does not fit is the answer.
- Confirm: with the correct value, the whole series works, including the next term.
One wrong term spoils two gaps
A wrong term makes both the gap before it and the gap after it look wrong.
Example: 5, 9, 13, 17, 22, 25. The gaps are 4, 4, 4, 5, 3. The bad gaps 5 and 3 sit around 22. So 22 is wrong. The correct value is 21.
Look for the term between two bad gaps.
Wrong terms by kind of series
Wrong term in a gap series. Take 3, 5, 9, 15, 23, 34, 45. The gaps are 2, 4, 6, 8, 11, 11. The expected gaps are 2, 4, 6, 8, 10, 12. So 34 should be 33.
Wrong term in a ratio series. In 2, 6, 18, 54, 164, 486, the rule is ×3. The term after 54 should be 162, not 164.
For ×k ± r, find each term from the term before it. In 5, 11, 23, 48, 95 the rule is ×2 + 1. Then 23 × 2 + 1 = 47, so 48 is wrong.
Watch: The term after a wrong term comes from the correct value. So 95 = 47 × 2 + 1 looks wrong if you use 48. Rebuild from the start.
Wrong term in squares and cubes. In 1, 8, 27, 64, 124, 216, the term 124 should be 125, which is 5³. In 2, 6, 12, 20, 31, 42, the rule is n × (n + 1), so 31 should be 30. Numbers just off a square or a cube are strong hints.
Wrong term in an alternate series. Split into odd and even places. In 2, 10, 4, 13, 6, 16, 9, 19, the odd places are 2, 4, 6, 9. They should be 2, 4, 6, 8. The even places 10, 13, 16, 19 are fine, so 9 is wrong.
Wrong term in a letter series. The same idea works with letters. In BD, EG, HJ, KN, NP, each cluster has an inner gap of 2. Only KN has a gap of 3. So KN is wrong and should be KM.
A full walk-through
Find the wrong term: 4, 7, 13, 25, 50, 97
- Guess the rule from the first terms. 4 × 2 − 1 = 7 and 7 × 2 − 1 = 13.
- Apply it on. 13 × 2 − 1 = 25. Then 25 × 2 − 1 = 49.
- The series shows 50, not 49. The next term, 97, equals 49 × 2 − 1.
- So 50 is the wrong term.
Tip: If the next term fits the correct value, you have found the culprit.
Speed tips
- The options are terms of the series. Test only the option terms.
- If all terms but one are odd, that one is suspect. Confirm with the rule.
- The first or last term can be the wrong one.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Wrong term in an equal-gap or growing-gap series
The terms grow slowly, and the gaps are nearly equal or nearly in order.
Write the gaps.
Find the two bad gaps.
The term between them is the wrong term.
A wrong term changes two neighbouring gaps.
Find the wrong term: 8, 12, 16, 21, 24, 28
Show solutionHide solution
Gaps: 4, 4, 5, 3, 4.
The bad gaps 5 and 3 sit around 21.
The rule is +4, so 21 should be 20.
21
Wrong term in a ratio or multiply-and-add series
The terms double or triple, and one term is a little off.
Find the ratio from the first terms.
Build each term from the term before it.
Find where the built value differs.
The near-miss shows itself as soon as you multiply.
Find the wrong term: 3, 6, 12, 25, 48, 96
Show solutionHide solution
The rule is ×2.
3, 6, 12, then 24. The series shows 25.
48 and 96 match the rule.
25
Wrong term in a squares or cubes series
The terms are close to squares or cubes, and one is just off.
List the squares or cubes.
Compare each term.
The one that is off by a little is the answer.
A square or cube list is fixed, so a slip stands out.
Find the wrong term: 4, 9, 16, 25, 35, 49
Show solutionHide solution
The terms are 2², 3², 4², 5², ?, 7².
The fifth term should be 6² = 36.
The series shows 35.
35
Wrong term in an alternate series
The gaps zigzag up and down. There are two tracks.
Split into odd and even places.
Check each track.
The track with a break holds the wrong term.
Each track is a simple series, so a slip is easy to spot.
Find the wrong term: 1, 20, 3, 18, 5, 17, 7
Show solutionHide solution
Odd places: 1, 3, 5, 7. They add 2.
Even places: 20, 18, 17. They should take away 2 each time.
The third even term should be 16. The series shows 17.
17
Wrong term in a letter series
The terms are letters or letter clusters, and one step is off.
Write the places.
Find the step.
Find the letter that breaks the step.
Letters are numbers, so the number method still works.
Find the wrong term: C, F, I, M, O
Show solutionHide solution
Places: 3, 6, 9, 13, 15.
The rule is +3: 3, 6, 9, 12, 15.
The fourth place should be 12, which is L. The series shows M.
M
Wrong term in a gaps-of-gaps series
The gaps rise in a pattern like 2, 4, 6, 8, and one gap breaks it.
Write the gaps.
Write the expected gaps.
Find the term between the two gaps that differ.
The expected gap pattern shows where the slip is.
Find the wrong term: 3, 5, 9, 15, 23, 34, 45
Show solutionHide solution
Gaps: 2, 4, 6, 8, 11, 11.
The expected gaps are 2, 4, 6, 8, 10, 12.
The bad gaps sit around 34. It should be 33.
34
The first term is wrong
The first gap looks odd, but all the other gaps agree.
Write the gaps.
If all gaps but the first agree, the first term is wrong.
Check that it is not the second term.
Only one gap is bad, because the first term has just one neighbour.
Find the wrong term: 13, 24, 33, 42, 51
Show solutionHide solution
Gaps: 11, 9, 9, 9.
Only the first gap is bad.
The first term should be 15. The series shows 13.
13
Shortcuts that save time
Write the gaps. Find two bad gaps side by side. The term between them is the wrong term.
Find the wrong term: 12, 15, 18, 22, 24, 27
Show solutionHide solution
Gaps: 3, 3, 4, 2, 3.
The bad gaps 4 and 2 sit around 22.
The rule is +3, so 22 should be 21. The wrong term is 22.
22
Mistakes to avoid
Where most students lose marks on this subtopic.
Giving the correct value as the answer.
The answer is the wrong term as it is shown in the question.
Blaming the term after the first bad gap.
The wrong term sits between two bad gaps.
Testing the rule only on the last few terms.
Test it from the first term. The first term can also be wrong.
Using the wrong term to build the next term.
Rebuild each term from the correct one, starting from the beginning.
Missing an alternate series.
If the gaps zigzag, split into odd and even places.
Quick revision
Read this the night before the exam.
The wrong term sits between two bad gaps.
Answer = the wrong term as shown, not its correct value.
Rebuild each term from the correct one before it.
Near misses like 124 for 125 and 31 for 30 are giveaways.
Up-and-down series: split into two series.
You can test just the option terms.
Practice: 14 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 10 questions
Suggested time 7 min · wrong answers go to your mistake notebook automatically.