ExamShortcut
🔍Log in

Series (Number & Letter)

🔒 Log in to track
high importance~4 Q in Tier 18 formulas⚡ 12 shortcuts6 subtopics
OverviewLearn (6)Formulas (8)Examples (4)Practice (95)
All subtopics·Subtopic 3 of 6

Letter series

🔒 Log in to track
⏱ 5 min read🧩 7 question types🎯 17 practice Q
The idea in one minute

Every letter series is a number series in disguise. Give each letter its place in the alphabet, then solve it as a number series. Go back to letters at the end, and wrap around after Z.

01

Letters are numbers in disguise

Give each letter its place in the alphabet: A = 1, B = 2, up to Z = 26. Then C, G, K, O becomes 3, 7, 11, 15. Each term adds 4, so the next is 19, which is S.

02

Learn the anchor letters

Counting from A each time is slow. Remember five anchors.

EJOTY
510152025

Every letter is one or two steps from an anchor. M is 2 less than O, so M = 13. R is 2 less than T, so R = 18.

Rule: The opposite of a letter is at place 27 minus its place. A and Z, B and Y, C and X, up to M and N. Each pair adds up to 27.

03

Wrap around after Z

After Z the alphabet starts again at A. If the place goes above 26, subtract 26.

Example: X is 24. Add 4 to get 28. Then 28 − 26 = 2, which is B.

Going back below A, add 26. C is 3. Take away 5 to get −2. Then −2 + 26 = 24, which is X.

04

Five kinds of letter series

Constant step. Every letter moves by the same amount. C, G, K, O, S adds 4. Z, W, T, Q takes away 3. T, W, Z, C, F crosses Z, because 26 + 3 = 29 and 29 − 26 = 3.

Rising or falling step. The step itself changes. In C, D, F, I, M the steps are +1, +2, +3, +4. The next step is +5, so the next letter is R. In Y, W, T, P, K the steps are −2, −3, −4, −5. The next step is −6, so the letter is E.

Two series mixed. Odd places make one series and even places make another. In A, Z, C, X, E, V the odd places are A, C, E (+2). The even places are Z, X, V (−2).

Or the steps take turns. In B, E, D, G, F, I the steps are +3, −1, +3, −1.

Letter clusters. A cluster is a group of two to four letters, like BDF, GIK, LNP. Each slot is its own series. First letters B, G, L add 5. So do the second and third slots. The next cluster is QSU.

Slots may move in different directions. In AZ, CX, EV the first letter adds 2 and the second takes away 2.

Positions follow a number pattern. The positions may be squares or primes.

  • A, D, I, P, Y are places 1, 4, 9, 16, 25.
  • B, C, E, G, K are places 2, 3, 5, 7, 11.

Tip: If the steps look random, write the places and check squares and primes.

05

A full walk-through

Find the next letter: K, M, P, T, Y, ?

  1. Places: 11, 13, 16, 20, 25.
  2. Steps: +2, +3, +4, +5. The next step is +6.
  3. 25 + 6 = 31. That is above 26, so 31 − 26 = 5.
  4. Place 5 is E.

Watch: Without the wrap-around, you would look for place 31. No such letter exists.

06

The four steps

  1. Write the place under each letter, using the anchors.
  2. Find the number rule with the gap ladder.
  3. Apply the rule. Wrap around if the place is above 26 or below 1.
  4. Change the number back to a letter.
07

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

Single letters with a constant step

How to spot it:

Each letter moves the same number of places. It may go forward, go backward or cross Z.

Method

  1. Write the place under each letter.

  2. Find the equal step.

  3. Add the step to the last place. Wrap around if it is above 26.

  4. Convert to a letter.

Why it works:

A constant step is an equal-gap number series.

Try this

Find the next letter: D, H, L, P, ?

Show solution

  1. Places: 4, 8, 12, 16.

  2. Each step is +4.

  3. 16 + 4 = 20, which is T.

Answer

T

Type 2very common3 practice Q

Rising or falling step between letters

How to spot it:

The gaps between places grow or shrink by one each time.

Method

  1. Write the places.

  2. Write the steps. They rise or fall evenly.

  3. Take the next step.

  4. Add it to the last place and convert.

Why it works:

The steps are the gaps ladder, just on letters.

Try this

Find the next letter: A, C, F, J, O, ?

Show solution

  1. Places: 1, 3, 6, 10, 15.

  2. Steps: +2, +3, +4, +5. The next step is +6.

  3. 15 + 6 = 21, which is U.

Answer

U

Type 3common2 practice Q

Two letter series mixed together

How to spot it:

The letters go forward and backward by turns, or two clear tracks are visible.

Method

  1. Write odd places and even places as two lines.

  2. Solve each line.

  3. Check which line the asked place belongs to.

  4. Extend that line only.

Why it works:

Two easy series woven together look like one hard series.

Try this

Find the next letter: B, Y, D, W, F, U, ?

Show solution

  1. Odd places: B, D, F. They add 2.

  2. Even places: Y, W, U. They take away 2.

  3. The seventh letter is an odd place. F + 2 = H.

Answer

H

Type 4very common3 practice Q

Letter-cluster series

How to spot it:

Each term is a group of two to four letters, and each slot changes by its own step.

Method

  1. Write the places of the first slot in every cluster.

  2. Find its step. Do the same for the second slot.

  3. Apply each step to make the next cluster.

Why it works:

Every slot is a small series of its own.

Try this

Find the next cluster: AC, EG, IK, ?

Show solution

  1. First letters: A, E, I add 4. The next is M.

  2. Second letters: C, G, K add 4. The next is O.

  3. The cluster is MO.

Answer

MO

Type 5occasional2 practice Q

Positions that are squares or primes

How to spot it:

The steps look random, but the places are famous numbers.

Method

  1. Write the places.

  2. Check if they are squares (1, 4, 9, 16) or primes (2, 3, 5, 7, 11).

  3. Take the next number in that list.

  4. Convert it to a letter.

Why it works:

The rule sits in the places, not in the steps.

Try this

Find the next letter: C, E, G, K, M, ?

Show solution

  1. Places: 3, 5, 7, 11, 13.

  2. These are primes. The next prime is 17.

  3. Place 17 is Q.

Answer

Q

Type 6common

A missing letter in the middle

How to spot it:

A blank sits inside the series, like F, I, ?, O, R.

Method

  1. Write the places of the visible letters.

  2. Find the rule from both sides of the blank.

  3. Fill the blank.

  4. Check the letter after the blank.

Why it works:

The letters on both sides fix the rule.

Try this

Find the missing letter: F, I, ?, O, R

Show solution

  1. Places: 6, 9, ?, 15, 18. Each step is +3.

  2. ? = 9 + 3 = 12, which is L.

  3. Check: 12 + 3 = 15.

Answer

L

Type 7occasional

Clusters that cross Z

How to spot it:

A slot moves past Z and starts again from A.

Method

  1. Write the places of each slot.

  2. Find each step.

  3. If a place goes above 26, subtract 26.

  4. Convert and join the slots.

Why it works:

Wrap-around matters most in clusters, because it is easy to forget in one slot.

Try this

Find the next cluster: XB, AD, DF, ?

Show solution

  1. First letters: X = 24, then 27 − 26 = 1 = A, then D. The step is +3, so the next is G.

  2. Second letters: B, D, F add 2. The next is H.

  3. The cluster is GH.

Answer

GH

08

Formula sheet

Opposite letter
place of opposite=27−place\text{place of opposite} = 27 - \text{place}

A and Z, B and Y, and so on. Each pair adds up to 27.

Wrap around
place>26⇒place−26,  place<1⇒place+26\text{place} > 26 \Rightarrow \text{place} - 26,\ \ \text{place} < 1 \Rightarrow \text{place} + 26

Use this whenever the rule takes you past Z or before A.

09

Shortcuts that save time

⚡ A step row under the letters

Write the place under every letter, then the gap between places. Work on the numbers only. Convert to a letter once, at the end.

Example

Find the next letter: H, J, L, N, ?

Show solution

  1. Places: 8, 10, 12, 14.

  2. Each gap is 2, so the next place is 16.

  3. Place 16 is P.

Answer

P

⚡ Wrap around with the number 26

Never count letters on your fingers past Z. Add or subtract 26 on the number, then convert.

Example

Find the letter that is 15 places after Q.

Show solution

  1. Q is 17. 17 + 15 = 32.

  2. 32 − 26 = 6.

  3. Place 6 is F.

Answer

F

10

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Counting on your fingers from A each time.

Use the anchors E, J, O, T, Y and count one or two steps from the nearest.

Mistake 02

Forgetting to wrap around after Z.

If the place is above 26, subtract 26 before you convert to a letter.

Mistake 03

Solving a cluster as one long series.

Solve each letter slot as its own series.

Mistake 04

Reading a jumpy series as one series.

Split it into odd and even places, or check for steps that take turns.

Mistake 05

Mixing up forward places and reverse places.

A = 1 counting forward. Z = 1 counting backward. Reverse place = 27 − place.

11

Quick revision

Read this the night before the exam.

  • A = 1 to Z = 26. Anchors: E 5, J 10, O 15, T 20, Y 25.

  • Opposite letters add up to 27.

  • Above 26: subtract 26. Below 1: add 26.

  • Clusters: solve each slot on its own.

  • Jumpy series: split into odd and even places.

  • Squares (A, D, I, P, Y) and primes (B, C, E, G, K) are favourite hidden rules.

12

Practice: 17 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 5 min · wrong answers go to your mistake notebook automatically.

Continue learning