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Reasoning · Chapter 3

Series

Number, letter and alphanumeric. The most reliably repeated topic in the whole reasoning section — eight of the questions in this chapter came straight out of the 2021 and 2025 papers.

Concept video — watch on the AAI ATC Exam Prep channel
3–4questions per shift
40 sectarget time each
4series types
8verified PYQs inside
Objectives 1. Number series 2. Letter series 3. Alphanumeric 4. Letter-number clusters 5. Wrap-around traps Summary Assessment Free PDF
Before you start

Learning objectives and outcomes

Every series question in every AAI paper is solved by one habit: write the differences underneath, and treat each position as its own separate series.

Objective 1Build a difference row, and a second difference row when the first is not constant.
Objective 2Split a letter series into columns and solve each column independently.
Objective 3Handle alphanumeric clusters where letters and numbers follow completely unrelated rules.
Objective 4Manage wrap-around past Z, which is where AAI plants its hardest options.
Outcome ASolve a four-term letter-number cluster in 40 seconds.
Outcome BRecognise a prime or square sequence hiding inside the number half of a cluster.
Subtopic 1

Number series — differences, then second differences

Write the gaps between consecutive terms in a row underneath. If those gaps are constant, you are done. If not, write the gaps between the gaps. Almost every AAI number series resolves at this second level.

The two-row method

Series:   100   120   145   180   235   ?
Row 1:      20    25    35    55
Row 2:         5     10    20    40

Row 2 doubles each time, so the next second difference is 40, the next first difference is 55 + 40 = 95, and the answer is 235 + 95 = 330.

Figure 3.1 — The two-row difference layout The series written across the top with the first difference row and second difference row stacked beneath, arrows showing how the answer is built back up. Upload image here
✈ AAI ATC relevance — number and letter series appeared three to four times in every shift analysed from 2021 to 2025
Memory trick — "Two rows, then think"

Do not look for a clever pattern before you have written both difference rows. Nine times out of ten the pattern is sitting in row two and needed no cleverness at all.

EasyATC Pattern
What comes next: 7, 12, 19, 28, 39, ?
The first differences are 5, 7, 9, 11, rising by 2 each time. The next difference is 13, so the answer is 39 + 13 = 52.
ModeratePYQ 2021 · Shift 3
Select the number that can replace the question mark: 100, 120, 145, 180, 235, ?
First differences are 20, 25, 35, 55. Second differences are 5, 10, 20 — doubling. The next second difference is 40, giving a first difference of 95, so the answer is 235 + 95 = 330.
HardATC Pattern
What comes next: 3, 7, 16, 35, 74, ?
Differences alone do not settle this one. Test a multiply-and-add rule instead: 3 × 2 + 1 = 7, 7 × 2 + 2 = 16, 16 × 2 + 3 = 35, 35 × 2 + 4 = 74. The added number rises by one each step, so next is 74 × 2 + 5 = 153.
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Subtopic 2

Letter series — solve each column separately

Given OA, LG, IM, FS, ? the instinct is to read each pair as a unit. Do the opposite. Stack the terms vertically and treat the first letters as one series and the second letters as another. They almost never share a rule.

Stack, convert, solve down each column

O A  →  15   1
L G  →  12   7
I M  →   9   13
F S  →   6   19
? ?  →   3   25  =  C Y

Column one falls by 3 each time, column two rises by 6 each time. Neither knows the other exists — and that independence is the whole technique.

Figure 3.2 — Column method for letter series Four two-letter terms stacked vertically with position numbers beside them, a downward arrow labelled −3 on the left column and +6 on the right. Upload image here
Memory trick — "Stack it, don't read it"

Never read a letter series left to right as words. Write the terms one under the other and work down each column. It converts a puzzle into two easy arithmetic sequences.

Worked example — 2021 Shift 2 paper

XY, RT, LO, FJ, ?

  1. Column one: X = 24, R = 18, L = 12, F = 6. Falling by 6.
  2. Next would be 6 − 6 = 0, which is not a position. Wrap backwards: 0 becomes 26, which is Z.
  3. Column two: Y = 25, T = 20, O = 15, J = 10. Falling by 5, so next is 5 = E.
  4. Answer: ZE. The wrap in column one is the entire difficulty — three options are built around getting it wrong.
EasyATC Pattern
What comes next: AC, EG, IK, MO, ?
Column one runs A, E, I, M — that is 1, 5, 9, 13, rising by 4, so next is 17 = Q. Column two runs C, G, K, O — 3, 7, 11, 15, also rising by 4, so next is 19 = S. The answer is QS.
ModeratePYQ 2021 · Shift 3
Select the letter-cluster that can replace the question mark: OA, LG, IM, FS, ?
Column one is 15, 12, 9, 6 — falling by 3, so next is 3 = C. Column two is 1, 7, 13, 19 — rising by 6, so next is 25 = Y. The answer is CY. Options A and C get column two wrong by one step in either direction.
HardPYQ 2021 · Shift 2
Select the letter-cluster that can replace the question mark: XY, RT, LO, FJ, ?
Column one falls by 6 from X, reaching 0 after F, which wraps round to Z. Column two falls by 5 from Y, reaching E. The answer is ZE. Option 3 comes from wrapping to A instead of Z, which is the most common error.
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Subtopic 3

Alphanumeric clusters

A letter attached to a number, like F5, J8, R14, D23. The letter half and the number half follow completely separate rules, and the number half is often not a simple difference at all — it can be primes, squares or a doubling gap.

Two independent series, always

Letters: F → J → R → D  ·  jumps of +4, +8, +12, +16
Numbers: 5 → 8 → 14 → 23  ·  gaps of +3, +6, +9, +12

Both halves grow, but at different rates. Solve one, then the other, then combine. Never assume the number tells you anything about the letter.

Figure 3.3 — Splitting an alphanumeric cluster The four terms with a vertical dividing line, letters and their jumps on the left, numbers and their gaps on the right. Upload image here
Memory trick — "Two pens, two series"

Physically separate the letters from the numbers on your rough sheet before you compute anything. Mixing them on one line is how the two rules get confused.

Worked example — 2021 Shift 2 paper

F5, J8, R14, D23, ?

  1. Letters: F = 6, J = 10, R = 18, D = 4. The jumps are +4, +8, and then 18 + 12 = 30, which wraps to 30 − 26 = 4 = D. So the jumps are +4, +8, +12.
  2. The next jump is +16: 4 + 16 = 20 = T.
  3. Numbers: 5, 8, 14, 23. The gaps are +3, +6, +9, so the next gap is +12.
  4. 23 + 12 = 35.
  5. Answer: T35.
EasyATC Pattern
What comes next: B4, D8, F12, H16, ?
Letters run B, D, F, H — positions 2, 4, 6, 8, rising by 2, so next is 10 = J. Numbers run 4, 8, 12, 16, rising by 4, so next is 20. The answer is J20.
ModeratePYQ 2021 · Shift 2
Select the alphanumeric-cluster that can replace the question mark: F5, J8, R14, D23, ?
Letters jump +4, +8, +12 with a wrap past Z between R and D, so the next jump of +16 gives T. Numbers rise by 3, 6, 9, so the next gap of 12 gives 35. The answer is T35.
HardPYQ 2021 · Shift 3
Select the alphanumeric-cluster that can replace the question mark: Y11, S7, M5, G3, ?
Letters are 25, 19, 13, 7 — falling by 6, so the next is 1 = A. The numbers 11, 7, 5, 3 are not an arithmetic sequence at all: they are consecutive primes running downwards, so the next is 2. The answer is A2. Anyone who forces a difference rule onto the numbers lands on option 2.
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Subtopic 4 · highest yield

Letter-number clusters — three letters plus a number

This is the 2025 signature format: BTE9 DQI12 FNM15 HKQ18 ? Four independent series in one question — three letter columns and one number column. It looks heavy and is actually the most mechanical question on the paper.

Four columns, four rules

B T E  9  →   2   20    5    9
D Q I 12  →   4   17    9   12
F N M 15  →   6   14   13   15
H K Q 18  →   8   11   17   18
?          →  10    8   21   21 = J H U 21

Column one rises by 2, column two falls by 3, column three rises by 4, and the number rises by 3. Write all four rules down before you look at a single option.

Figure 3.4 — Four-column breakdown The four cluster terms written in a grid with each column's rule written underneath in a coloured band. Upload image here
Memory trick — "Grid it out"

Draw an actual four-column grid on your rough sheet. The extra five seconds of setup makes all four rules visible at once, and you will never mix up column two with column three again.

ModeratePYQ 2025 · Shift 1
Which letter-number cluster will replace the question mark to make the series logically complete? BTE9, DQI12, FNM15, HKQ18, ?
Column one B, D, F, H rises by 2 to J. Column two T, Q, N, K falls by 3 to H. Column three E, I, M, Q rises by 4 to U. The number rises by 3 to 21. The answer is JHU21.
ModeratePYQ 2025 · Shift 2
Which letter-number cluster will replace the question mark to make the series logically complete? BDQ8, DGO12, FJM16, HMK20, ?
Column one B, D, F, H rises by 2 to J. Column two D, G, J, M rises by 3 to P. Column three Q, O, M, K falls by 2 to I. The number rises by 4 to 24. The answer is JPI24.
HardPYQ 2025 · Shift 2
What should come in place of the question mark, based on English alphabetical order? BDF, EFI, HHL, KJO, ?
Column one B, E, H, K rises by 3 to N. Column two D, F, H, J rises by 2 to L. Column three F, I, L, O rises by 3 to R. The answer is NLR. Note that two columns share a rule of +3 here — that similarity is what makes the middle column easy to miss.
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Subtopic 5

Wrap-around and the traps AAI builds

When a letter column runs past Z going forwards, or past A going backwards, you wrap. Getting the wrap off by one is the single most common way candidates lose a series mark, and the wrong options are designed around exactly that error.

Wrapping in both directions

Going forward:   if position > 26, subtract 26
Going backward:   if position < 1, add 26

The one that catches people is landing on zero. Position 0 is not A — it is Z, because 0 + 26 = 26. In the 2021 Shift 2 question, column one lands on exactly 0, and option 3 exists purely for candidates who answer A.

A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13
N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26
Figure 3.5 — Wrapping past Z and back to A A circular alphabet with two arrows: one running forward past Z into A, one running backward past A into Z, with the zero position marked as Z. Upload image here
Memory trick — "Zero is Z, not A"

Say it once before every series question. It is worth roughly one mark per paper on its own.

EasyATC Pattern
A letter column falls by 4 from H. What is the letter two steps later?
H is 8. One step of −4 gives 4 = D. A second step gives 0, which wraps by adding 26 to become 26 = Z. Landing on zero is the trap; zero is Z, never A.
ModerateATC Pattern
What comes next: W, B, G, L, ?
W is 23, and adding 5 gives 28, which wraps to 2 = B. B to G is +5, G to L is +5, so the next is L = 12 plus 5 = 17 = Q. The wrap happens at the start rather than the end, which is why the rule is easy to miss.
HardATC Pattern
What comes next: P3, K5, F7, A11, ?
Letters are 16, 11, 6, 1 — falling by 5, so the next is 1 − 5 = −4, which wraps by adding 26 to give 22 = V. The numbers 3, 5, 7, 11 are consecutive primes, so the next is 13. The answer is V13. Option 1 comes from wrapping to 23 instead of 22, and option 2 from forcing an arithmetic rule onto the primes.
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Exam strategy

Six tips that hold in the AAI ATC hall

Write both difference rowsBefore you think about anything clever. Row two usually holds the answer.
Stack, never read acrossLetter series are columns. Turn them vertical on the rough sheet.
Grid the four-column clustersFive seconds of setup prevents the commonest mix-up in the format.
Numbers may be primesIf differences fail on the number half, check primes and squares next.
Zero is ZNot A. This alone is worth a mark most papers.
Confirm on two columnsOnce two columns agree with an option, pick it and move on.
Quick revision

Chapter summary sheet

Number seriesFirst differences, then second differences. Then multiply-and-add.
2021 Shift 3100, 120, 145, 180, 235 → second differences double → 330.
Letter seriesStack vertically, solve each column as its own sequence.
2021 Shift 3OA, LG, IM, FS → columns −3 and +6 → CY.
2021 Shift 2XY, RT, LO, FJ → columns −6 and −5, with a wrap → ZE.
AlphanumericLetters and numbers are unrelated. Split them physically.
Prime numbersY11, S7, M5, G3 → the numbers are descending primes → A2.
2025 formatThree letter columns plus a number column. Four rules, one grid.
WrappingOver 26, subtract 26. Under 1, add 26. Zero is Z.

↓ Free download — Series question PDF

Four pages of practice covering all four series types, with a printable alphabet-position strip and ruled grid space for your column working. Print it, solve it, keep it.

End of chapter

Comprehensive assessment

Multiple choice and assertion–reason, building in difficulty. Full solutions are in the downloadable PDF above.

A · Multiple choice questions

1. What comes next: 7, 12, 19, 28, 39, ?
2. What comes next: 5, 11, 23, 47, 95, ?
3. What comes next: 100, 120, 145, 180, 235, ? PYQ 2021 · Shift 3
4. What comes next: 3, 7, 16, 35, 74, ?
5. What comes next: AC, EG, IK, MO, ?
6. What comes next: OA, LG, IM, FS, ? PYQ 2021 · Shift 3
7. What comes next: XY, RT, LO, FJ, ? PYQ 2021 · Shift 2
8. What comes next: B4, D8, F12, H16, ?
9. What comes next: F5, J8, R14, D23, ? PYQ 2021 · Shift 2
10. What comes next: Y11, S7, M5, G3, ? PYQ 2021 · Shift 3
11. What comes next: BTE9, DQI12, FNM15, HKQ18, ? PYQ 2025 · Shift 1
12. What comes next: BDQ8, DGO12, FJM16, HMK20, ? PYQ 2025 · Shift 2
13. What comes next: BDF, EFI, HHL, KJO, ? PYQ 2025 · Shift 2
14. What comes next: W, B, G, L, ?
15. What comes next: P3, K5, F7, A11, ?

B · Assertion and reason

16. Assertion: A letter position of zero corresponds to Z. Reason: When a backward count falls below 1, you add 26 to recover the position.
17. Assertion: In an alphanumeric cluster, the number half can be used to predict the letter half. Reason: Both halves of a cluster always follow the same rule.
18. Assertion: Second differences should be computed before searching for a multiply-and-add rule. Reason: Most AAI number series resolve at the second-difference level.
19. Assertion: A four-column cluster question needs four separate rules. Reason: Each column is an independent series that ignores the others.
20. Assertion: If the differences in the number half of a cluster are not constant, the sequence has no rule. Reason: Every exam sequence must be arithmetic.
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