How to Solve Number Series Questions: 7 Rules to Check
Here's how to solve number series questions: write down the gap between each pair of numbers, then check a short list of rules in the same order every time. Adding, multiplying, squares, doubling gaps, alternating series, position rules and mixed operations cover almost every number sequence you'll see on an IQ test. The fixed order is the trick, because it stops you staring at the numbers and hoping.
If you freeze or rush on number patterns, IQ Tester pins down whether it's pattern spotting, mental arithmetic or something else, and trains that exact slip: Find my weak spots.
Start with the gaps
Most people look at a number series and wait for the answer to jump out. Sometimes it does. When it doesn't, the fastest move is to stop looking at the numbers and look at the spaces between them.
Take 3, 7, 15, 31, ?
Write the differences underneath:
- 7 − 3 = 4
- 15 − 7 = 8
- 31 − 15 = 16
The gaps are 4, 8, 16. They double. So the next gap is 32, and the answer is 31 + 32 = 63.
That's the whole difference method. Even when the gaps don't give you the answer straight away, they tell you which rule to try next. Big, fast-growing gaps point to multiplication. Gaps that bounce up and down point to an alternating series. Gaps that grow by a steady amount point to squares.
Number series tips before you start
- Write the gaps on paper or in your head as a second row. Don't skip this.
- Say the gaps out loud, even under your breath. "4, 8, 16" is easier to spot than the original row.
- If the gaps don't make sense, take the gaps of the gaps. That second row often reveals the pattern.
Rule 1-2: add or multiply
Check these two first, because they're the most common number series questions of all.
Rule 1: the same amount is added (or taken away)
5, 12, 19, 26, ? Gaps: 7, 7, 7. Answer: 33.
Easy when you see it. The only catch is negative steps: 50, 44, 38, 32, ? has gaps of −6, so the answer is 26.
Rule 2: the same amount is multiplied (or divided)
2, 6, 18, 54, ? Gaps: 4, 12, 36. They're growing fast, which is your hint. Divide instead: 6 ÷ 2 = 3, 18 ÷ 6 = 3. Each number is times 3, so the answer is 162.
Quick test: if the gaps are growing by a steady multiple, the series itself is multiplying. If a number series shrinks and the numbers divide cleanly (64, 32, 16, 8), think division.
Rule 3-4: squares, cubes and doubling gaps
If rules 1 and 2 fail, look for special numbers.
Rule 3: squares and cubes
Learn these by heart. They're the backbone of number series tricks:
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| n² | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |
| n³ | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | 1000 |
1, 4, 9, 16, ? is plain squares: 25.
A sneakier version shifts every square by one: 2, 5, 10, 17, 26, ? Each number is a square plus 1 (1+1, 4+1, 9+1...), so the answer is 36 + 1 = 37. Notice the gaps too: 3, 5, 7, 9. Gaps that climb by 2 are almost always a sign of squares.
Rule 4: gaps that change in a pattern
Sometimes the gaps themselves form a series. 1, 2, 4, 7, 11, ? has gaps 1, 2, 3, 4, so the next gap is 5 and the answer is 16.
Or the gaps double, like the 3, 7, 15, 31 example. When the first row of gaps looks messy, write the second row. That one extra line solves a surprising number of missing number series.
Rule 5: alternating series
When the gaps go up, down, up, down, you're probably looking at two series woven together.
4, 10, 6, 12, 8, 14, ?
Split it into odd and even positions:
- Positions 1, 3, 5: 4, 6, 8 (adding 2)
- Positions 2, 4, 6: 10, 12, 14 (adding 2)
The next number is position 7, which belongs to the first series. Answer: 10.
Alternating series also mix operations. 3, 5, 6, 10, 12, 20, ? is two strands: 3, 6, 12 (doubling) and 5, 10, 20 (doubling). Next is 24.
The same trick works for letters. If you like this kind of puzzle, the two-strand idea shows up again in letter series questions.
Doing this alone, it's hard to tell whether you missed an alternating series because you didn't know the rule or because you rushed. IQ Tester's 16-question check separates those two, then gives you one short daily drill aimed at whichever it was, like "Estimate first" or "Name the rule out loud." Find my weak spots
Rule 6-7: position and mixed operations
These are the rules that make a number sequence puzzle feel "impossible" until you see it.
Rule 6: the number depends on its position
Here, each term comes from its place in the line (1st, 2nd, 3rd...), not from the term before it.
2, 6, 12, 20, 30, ? Look at it as 1×2, 2×3, 3×4, 4×5, 5×6. The next is 6×7 = 42.
Another family: each term is made from the two before it. 1, 1, 2, 3, 5, 8, ? is the Fibonacci sequence, where you add the last two numbers: 13. That one shows up so often it has its own post: Fibonacci sequence riddles.
Rule 7: two steps in a row
The toughest number pattern questions use two operations per step.
2, 5, 11, 23, 47, ? Gaps: 3, 6, 12, 24, which double. That works. But you can also see it as "times 2, plus 1": 2×2+1 = 5, 5×2+1 = 11. Either way the answer is 95.
3, 4, 10, 33, ? is harder. Try "times 1 plus 1, times 2 plus 2, times 3 plus 3": 3×1+1 = 4, 4×2+2 = 10, 10×3+3 = 33. Next: 33×4+4 = 136.
When you reach rule 7, try "multiply, then add something small." Most mixed series are built that way.
A timed routine for solving number series questions quickly
Knowing the rules is half of it. The other half is not panicking when the clock is running. Here's a routine you can use in any test.
The 60-second checklist
- Scan (5 seconds). Is it growing slowly, growing fast, shrinking, or bouncing?
- Write the gaps (10 seconds). One row. Say them out loud in your head.
- Check rules 1 to 7 in order. Add, multiply, squares/cubes, changing gaps, alternating, position, mixed.
- Test your answer against every number, not just the last two. A rule that fits only the end is a wrong rule.
- If you're past about 60 seconds, guess and move on. Mark it and come back if there's time.
Number series practice for beginners
Try these, then check the answers below.
- 7, 14, 28, 56, ?
- 1, 8, 27, 64, ?
- 20, 17, 21, 18, 22, ?
- 0, 3, 8, 15, 24, ?
- 1, 3, 7, 13, 21, ?
Answers: 1) 112 (times 2). 2) 125 (cubes). 3) 19 (alternating, −3 and +4). 4) 35 (squares minus 1). 5) 31 (gaps 2, 4, 6, 8, 10).
If one of these took you much longer than the others, notice which rule it was. That's your practice target. The fix for most people isn't more random number series questions; it's more of the one type that trips them up.
Find the number patterns that trip you up
You now know how to solve number series questions with a fixed order of checks. The next step is finding which rule you personally stall on. IQ Tester takes about two minutes and 16 questions to show you your reasoning tier and your weak spots, then gives you one tip and a 10-minute drill each day that leans toward them.
FAQ
How do you solve number series easily?
Write the gaps between each pair of numbers first, then check the rules in order: add, multiply, squares and cubes, changing gaps, alternating, position and mixed. Having a fixed order means you never waste time wondering where to start. Most beginners find the gaps alone solve about half the questions.
What are the best number series tricks for IQ tests?
Memorize squares up to 15² and cubes up to 10³, because spotting them instantly saves a lot of time. If gaps bounce up and down, split the series into odd and even positions. If gaps grow very fast, switch from subtraction to division.
How do I solve a missing number series when the gap is in the middle?
Work out the rule using the numbers on both sides of the blank. Check the gaps to the left of the gap and to the right, and make sure your answer fits both. A missing number in the middle is often easier than one at the end because you have more clues.
How can I solve number series questions quickly under time pressure?
Set a hard limit of about a minute per item and stick to the same checklist every time. Guess and move on if you pass the limit. Speed comes from recognizing rules quickly, which you build with short daily practice rather than long cram sessions.
Is there a number series quiz I can practice with?
Yes: the five-question practice set above is a good start. For daily practice that targets your own slip, IQ Tester includes number drills as part of its daily 10-minute session, weighted toward your weak spots.