Series — General Intelligence & Reasoning Notes for AAI Manager (Civil)

Part 1 of 2

Number Series

Last reviewed 22 Sept 2026 · 5 min read

A working order

Do these in order and stop at the first that works:

First differences. Constant → arithmetic. Growing → take the second differences; constant there means a quadratic pattern (often $n^{2}$ based).
Ratios. Constant → geometric. Nearly constant → multiply-and-add.
Squares, cubes and their neighbours: $n^{2}$ , $n^{2} \pm 1$ , $n^{3}$ , $n^{3} \pm n$ .
Primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) or their squares.
Alternating: two patterns interleaved — look at terms 1, 3, 5 and 2, 4, 6 separately.
Mixed operation: $\times 2 + 1$ , $\times 3 - 2$ , $+ 1 \times 2$ repeated.
Digit rules: sum of the digits added, digits reversed, digits multiplied.

Exam TipTwo seconds well spent

Before anything, notice whether the series grows slowly (differences — think arithmetic or squares) or explodes (ratios — think geometric, cubes or factorials). That single judgement removes half the possibilities.

The three question types

Type	What is asked	Method
Next term	continue the series	find the rule, apply it once more
Missing term	fill a gap in the middle	find the rule from the terms around the gap, then verify on the rest
Wrong term	one term breaks the rule	find the rule from the majority, then name the term that does not obey

In a wrong term question the answer is the term to be removed, not its correct replacement — read what the options represent.

Patterns worth recognising on sight

$2, 6, 12, 20, 30 \dots$ → $n (n + 1)$
$1, 4, 9, 16, 25 \dots$ → $n^{2}$ ; $2, 5, 10, 17, 26 \dots$ → $n^{2} + 1$
$1, 8, 27, 64 \dots$ → $n^{3}$ ; $0, 7, 26, 63 \dots$ → $n^{3} - 1$
$1, 1, 2, 3, 5, 8 \dots$ → Fibonacci (each term is the sum of the two before)
$1, 2, 6, 24, 120 \dots$ → factorials
$4, 9, 25, 49, 121 \dots$ → squares of primes
Differences that are themselves $2, 4, 6, 8$ or $1, 2, 3, 4$ → a quadratic rule

Part 2 of 2

Letter & Alphanumeric Series

Last reviewed 22 Sept 2026 · 5 min read

The alphabet, numbered

A = 1, B = 2, C = 3, \dots, Z = 26

RememberTwo facts that save the most time

EJOTY: E=5, J=10, O=15, T=20, Y=25. Any letter is now two steps away — P is one after O, so 16.
Opposite letters add to 27: A↔Z, B↔Y, C↔X, M↔N. So the opposite of G(7) is T(20).

Counting backwards from Z is the same as counting forwards with $27 - n$ .

Letter series

The usual rules, in the order worth testing:

Fixed shift: A, C, E, G … (+2 each time).
Growing shift: A, B, D, G, K … (+1, +2, +3, +4).
Two alternating shifts: A, D, C, F, E, H … (+3, −1, +3, −1).
From both ends: A, Z, B, Y, C, X … (one from the front, one from the back).
Groups with an internal rule: ABD, EFH, IJL … (+1, +2 inside each group; each group starts 4 after the last).
Repeated letters: a letter that reappears at fixed intervals, common in "complete the series" questions with a blank pattern such as ab _ aa _ bab _.

Alphanumeric series

A row mixing letters, digits and symbols, such as

5 P J 9 @ K 3 % T 7 R # 2 D

The questions are nearly always one of these:

Question	How to answer
Which is 5th from the left?	count from the left including everything
Which is 4th from the right?	count from the right, or use position $= n - k + 1$
Which is 3rd to the left of the 9th from the left?	$9 - 3 = 6$ th from the left
How many letters are immediately preceded by a digit?	scan left-to-right, checking each letter's left neighbour
How many symbols are immediately followed by a letter?	check each symbol's right neighbour

Exam TipThe direction trap

"Preceded by" means the item before it in the row; "followed by" means after it. Half the marks lost in this topic come from swapping the two — underline the word before you start scanning.

For " $k$ th from the right" in a row of $n$ items: it is the $(n - k + 1)$ th from the left.

Worked examples

Worked ExampleExample 1 — fixed shift

A, D, G, J, ?

Solution. Each letter moves 3 forward → M.

Worked ExampleExample 2 — growing shift

A, B, D, G, K, ?

Solution. Shifts are +1, +2, +3, +4 → next is +5 from K(11) → P(16) → P.

Worked ExampleExample 3 — from both ends

A, Z, C, X, E, V, ?

Solution. Odd places A, C, E rise by 2 → G; even places Z, X, V fall by 2 → T. The next term is at an odd place → G.

Worked ExampleExample 4 — groups

ABD, EFH, IJL, ?

Solution. Inside a group: +1, +2. Each group starts 4 letters after the previous start (A, E, I) → next starts at M → MNP.

Worked ExampleExample 5 — position arithmetic

Which letter is midway between the 8th letter from the left and the 14th from the left?

Solution. $\frac{8 + 14}{2} = 11$ → the 11th letter, K.

Worked ExampleExample 6 — opposite letters

What is the opposite of the letter that is 7th from the left?

Solution. 7th is G; opposite is $27 - 7 = 20$ → T.

Worked ExampleExample 7 — counting from the right

In the English alphabet, which letter is 5th to the right of the 12th letter from the right?

Solution. 12th from the right is $26 - 12 + 1 = 15$ th from the left, O. Five to the right → the 20th → T.

Worked ExampleExample 8 — alphanumeric, plain counting

For the row 5 P J 9 @ K 3 % T 7 R # 2 D (14 items), which item is 6th from the left, and which is 4th from the right?

Solution. 6th from the left is K. 4th from the right is the $14 - 4 + 1 = 11$ th from the left → R.

Worked ExampleExample 9 — preceded by a digit

In the same row, how many letters are immediately preceded by a digit?

Solution. Check each letter's left neighbour: P (after 5 ✓), J (after P ✗), K (after @ ✗), T (after % ✗), R (after 7 ✓), D (after 2 ✓) → 3.

Worked ExampleExample 10 — a symbol between a digit and a letter

In the same row, how many symbols are immediately preceded by a digit and immediately followed by a letter?

Solution. @ sits between 9 and K ✓; % sits between 3 and T ✓; # sits between R and 2 ✗ → 2.

Worked ExampleExample 11 — a repeating pattern

Fill the blanks: a _ a a b _ a a a _ b b

Solution. Written out, the visible letters are one a, then two a's and two b's, then three a's — so the pattern is $1 a 1 b$ , $2 a 2 b$ , $3 a 3 b$ :

a b | a a b b | a a a b b b

The blanks are b, b, b.

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Number Series

A working order

The three question types

Patterns worth recognising on sight

Letter & Alphanumeric Series

The alphabet, numbered

Letter series

Alphanumeric series

Worked examples

Finished reading? Test yourself.