What comes next: 1, 1, 2, 3, 5, 8, 13…?

How to think about it

1. Look at how each number relates to its neighbors. 1 + 1 = 2, then 1 + 2 = 3, then 2 + 3 = 5.
2. The rule: every term is the sum of the previous two.
3. Check it on the last pair given: 5 + 8 = 13. The rule holds.
4. Apply it once more: 8 + 13 = 21.

Why “21” is the answer

This is the Fibonacci sequence, where each number is the sum of the two numbers before it, so after 8 and 13 comes 21. The pattern continues 34, 55, 89 and so on, and the ratio between neighbors gets closer and closer to the golden ratio. The hint about looking at the two numbers before each one gives away the rule.

Common wrong answers

• 18. Adding 5 to 13 assumes a constant difference, but the gaps are growing: 1, 1, 2, 3, 5.
• 26. Doubling 13 would fit a geometric sequence, but 2 × 8 is not 13.