Fibonacci & Beyond:
How to Spot Patterns in Number Sequences
You've seen them on IQ tests, in coding interviews, and in our daily puzzles: 2, 4, 8, 16, ?.
Solving number sequences isn't just about being "good at math." It's about inductive reasoning—the ability to look at specific examples and infer a general rule. It is a skill that can be trained.
Here is the systematic way to crack any number sequence, from the simple to the impossible.
Level 1: The "Difference" Check
The first thing you should always do is look at the gap between the numbers. Write down the difference between each term.
- Arithmetic Sequence: The gap is constant.
5, 8, 11, 14... (Gap is always +3). - Geometric Sequence: The numbers are being multiplied.
3, 6, 12, 24... (Gap is doubling).
Level 2: The "Gap of the Gap"
What if the gap changes?
2, 5, 10, 17, 26...
Let's find the differences:
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7
26 - 17 = 9
The gaps are 3, 5, 7, 9. The "gap of the gap" is always +2. This usually means the sequence involves squares (n²). Indeed, 2 is 1²+1, 5 is 2²+1, etc.
Level 3: The Fibonacci (The Nature Code)
This is the most famous pattern in nature, found in pinecones, sunflowers, and seashells.
1, 1, 2, 3, 5, 8, 13...
The Rule: Add the previous two numbers to get the next one.
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
💡 Pro Tip:
If you see a sequence that starts slow but grows moderately fast (but not as fast as multiplication), always check if it's a Fibonacci variation. For example: 2, 2, 4, 6, 10...
Level 4: Alternating Sequences
These are tricky because they look like chaos.
10, 2, 12, 4, 14, 6...
If the numbers go Up, Down, Up, Down... you are likely looking at two interleaved sequences.
- Sequence A (Odd positions): 10, 12, 14... (+2)
- Sequence B (Even positions): 2, 4, 6... (+2)
📋 Quick Reference Card
Constant gap between numbers
Multiplying by constant
Sum of previous two
Two interleaved patterns
Conclusion
Number sequences are everywhere—from IQ tests and job interviews to daily puzzles like ours. The key is to approach them systematically: check the gaps, then the gap of the gaps, then special patterns like Fibonacci.
With practice, you'll start recognizing these patterns instantly. Ready to test your skills?
❓ Frequently Asked Questions
What is the easiest way to solve number sequences?
Start by finding the difference between consecutive numbers. If the difference is constant, it's arithmetic. If the ratio is constant, it's geometric. For harder patterns, find the "difference of the differences."
How do I recognize a Fibonacci sequence?
Look for sequences where each number is the sum of the two preceding ones. Classic examples: 1, 1, 2, 3, 5, 8 or variations like 2, 2, 4, 6, 10.
Are number sequence puzzles good for brain training?
Yes! Research shows that pattern recognition exercises strengthen inductive reasoning, working memory, and cognitive flexibility—key skills for problem-solving in everyday life.
Test Your IQ Pattern Skills
Can you solve today's Number Sequence puzzle? You only get one guess!
▶ PLAY NUMBER SEQUENCE