Series (Number & Letter)
🔒 Log in to trackAlphanumeric series
🔒 Log in to trackAn alphanumeric term mixes a letter and a number, like A3 or D6. Most of the time the letters follow one series and the numbers follow another. Solve the two tracks separately, then join the answers in the same format as the terms.
What an alphanumeric series is
Each term holds a letter and a number, like A3, D6, G9. Think of seats in a train: the coach letter changes by one rule and the seat number by another.
Two independent tracks
Split every term into its letter and its number. Solve each as its own series. Then join.
Example: B2, D4, F8, H16, ? The letters B, D, F, H add 2, so the next is J. The numbers 2, 4, 8, 16 double, so the next is 32. Answer J32.
The number may come first. In 3Z, 7W, 11T the numbers add 4 and the letters go back 3. The next term is 15Q.
The number follows the letter
Sometimes the number is not a separate series. It is made from the letter's place. Check this first.
| Terms | Link |
|---|---|
| C3, F6, I9, L12 | Number = place of the letter |
| B4, D16, F36, H64 | Number = (place of the letter) squared |
| Z1, W8, T27, Q64 | Number is a cube, letters go back |
If the link holds for every term, find the next letter. The number follows from it.
Watch: If you need the number to work out the letter, or the letter to work out the number, check the link first. Otherwise keep the tracks apart.
Terms with two letters and a number
A term can carry two letters and a number, like AB2, DE4, GH8. Each letter slot is its own series. A, D, G add 3, and B, E, H add 3. The numbers double, so the next term is JK16.
The number can come first. In 2CZ, 4EX, 6GV the number adds 2, the first letter adds 2 and the last letter goes back 2.
A missing term in the middle
Find each track from the visible terms. Fill the gap and check the term after it.
Example: D5, G10, ?, M20, P25. The letters add 3, so the gap has J. The numbers add 5, so the gap has 15. The missing term is J15.
Number tracks to know
The number track often uses one of these.
| Track | Example |
|---|---|
| Add a fixed number | 5, 10, 15, 20 |
| Multiply by 2 or 3 | 3, 6, 12, 24 |
| Squares | 1, 4, 9, 16, 25 |
| Cubes | 1, 8, 27, 64, 125 |
Example: F3, I6, L12, O24, ? The letters F, I, L, O add 3, so the next is R. The numbers 3, 6, 12, 24 double, so the next is 48. Answer R48.
The method
- Draw one column for letters and one for numbers.
- Change letters to places, using the anchors E, J, O, T, Y.
- Find each rule: add, multiply, square, cube, or same as the place.
- Write the answer in the same format as the terms.
- Compare options that differ in one character.
Reading the options
Examiners set options like J30 and J32, or J32 and 32J. Only one option has the right letter, the right number and the right order. Check all three.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Letter and number as two independent tracks
The letters follow one visible series and the numbers follow another. Neither depends on the other.
Write letters in one column and numbers in another.
Find each rule.
Apply both rules to the last term.
Join in the same format.
Two simple series are easier than one mixed series.
Find the next term: K5, M10, O15, Q20, ?
Show solutionHide solution
Letters K, M, O, Q add 2. The next is S.
Numbers 5, 10, 15, 20 add 5. The next is 25.
The term is S25.
S25
Number equals the place of the letter
Every number equals the alphabet place of its letter.
Check that each number matches the place of its letter.
Find the step of the letters.
Find the next letter.
Its place is the number.
The number carries no new information, so only the letters need a rule.
Find the next term: E5, H8, K11, ?
Show solutionHide solution
E = 5, H = 8, K = 11. Numbers match places.
The letters add 3, so the next letter is N.
N = 14. The term is N14.
N14
Terms with two letters and a number
Each term has two letters and a number. Slots may move in different directions.
Solve the first letter.
Solve the second letter.
Solve the number.
Join in the same order.
Each slot is a small series of its own.
Find the next term: AZ1, BY2, CX3, ?
Show solutionHide solution
First letters A, B, C add 1. The next is D.
Second letters Z, Y, X go back 1. The next is W.
Numbers add 1. The next is 4. The term is DW4.
DW4
A missing term in the middle
A '?' is inside the series, with terms on both sides.
Find each track from the visible terms.
Fill the letter and the number.
Check the term after the gap.
The terms on both sides of the gap fix the rule.
Find the missing term: B3, E6, ?, K12, N15
Show solutionHide solution
Letters B, E, ?, K, N add 3. The missing letter is H.
Numbers 3, 6, ?, 12, 15 add 3. The missing number is 9.
The term is H9.
H9
Number equals the place squared
The numbers are 4, 16, 36, 64, which are squares of even places.
Write the place of each letter.
Compare each number with the square of the place.
Find the next letter.
Square its place.
The number is made from the letter, so find the letter first.
Find the next term: B4, D16, F36, H64, ?
Show solutionHide solution
B = 2, D = 4, F = 6, H = 8. The letters add 2.
The numbers are 2², 4², 6², 8². The next letter is J = 10.
10² = 100. The term is J100.
J100
Number comes first
The number is written before the letter, like 3Z, 7W, 11T.
Split each term into its number and its letter.
Solve the numbers and the letters separately.
Write the answer with the number first.
The format changes, but the method does not.
Find the next term: 3Z, 7W, 11T, ?
Show solutionHide solution
Numbers 3, 7, 11 add 4. The next is 15.
Letters Z = 26, W = 23, T = 20. Each takes away 3. The next is 17, which is Q.
The term is 15Q.
15Q
Shortcuts that save time
Write letters in one column and numbers in the other. Solve each column on its own. Join only at the end, in the format of the question.
Find the next term: E4, H8, K12, N16, ?
Show solutionHide solution
Letters: E, H, K, N add 3, so the next is Q.
Numbers: 4, 8, 12, 16 add 4, so the next is 20.
The term is Q20.
Q20
Check whether the number equals the place of the letter, or its square. If yes, you only need the next letter.
Find the next term: D4, G7, J10, ?
Show solutionHide solution
D = 4, G = 7, J = 10. The number is the place of the letter.
The letters add 3, so the next letter is M.
M = 13. The term is M13.
M13
Mistakes to avoid
Where most students lose marks on this subtopic.
Picking an option with the right letter but a number from a wrong rule.
Solve the number track on its own. Then match both parts.
Writing the answer in the wrong order, like 32J for J32.
Copy the format of the given terms.
Using the letter's step for the number, or the number's step for the letter.
Keep two separate columns. Each has its own step.
Not checking whether the number is the place of the letter.
Test this link first. It is a common rule.
Quick revision
Read this the night before the exam.
Split each term into a letter part and a number part.
Solve each track alone, then join in the same format.
Test 'number = place of the letter' and 'number = place squared' first.
Clusters: every letter slot is its own series.
Check all three parts of the option: letter, number and order.
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 6 min · wrong answers go to your mistake notebook automatically.