Concept 3 of 6
Mixed Series: Two Patterns at Once
Today's big idea
Split the letters from the numbers, solve each row on its own, then combine the answers.
Letters can climb while numbers fall, so never read a whole term at once.
How it works
👀 What's going on?
Some series pair a letter with a number in every single term. Two rules are running at once, one on each part. Read a term whole and you will never see either of them.
💡 Here's the trick
Look at the series above. Pull the letters into one row and the numbers into another. Now you have two ordinary series, and each one has its own rule. Solve them apart, then join the two answers back together.
🪄 How to do it
- 1.Split the letters from the numbers, as in the series above.
- 2.Find the rule for the letter row, then for the number row.
- 3.Take the next letter and next number, and write them as one term.
✍️ Try it
Find the next term in M6, N12, O24, P48, ? Then find the next term in W1, U3, S5, Q7, ?
The letters step +1 to Q and the numbers double to 96, giving Q96. In the second series the letters drop 2 to O and the numbers rise 2 to 9, giving O9.
⚠️ Watch out
You might be thinking both halves must move the same way. They often do not. Letters can climb while numbers fall, so check each row on its own before you decide.
🌟 Why this matters
Car number plates, bus routes and cinema tickets all pair a letter with a number, and each part counts on its own. Reading 14B as one lump tells you nothing, while reading it as row and seat takes you there.
Exam tip: Solve the letter row first, because it usually rules out two of the four choices straight away.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find the next term: K3, N6, Q12, T24, ?”
- 1
Split into two patterns
Letters: K, N, Q, T. Numbers: 3, 6, 12, 24. ✂️
- 2
Solve the letters
K, N, Q, T → +3 each → next W.
- 3
Solve the numbers
3, 6, 12, 24 double each time → next 48.
- 4
Recombine ✓
W48
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Never read the whole term at once. SPLIT into a letter track and a number track, step each by its own rule, then join.
MIXED SERIES · ROUND 1 OF 3
Quick check
✅ VERIFICATION
Find the next term: P3, R9, T27, V81, ?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Figure Series
Steady gap gives n's multiplier; figure 1 pins the rest.