Number Sequence Puzzles

Spot the pattern and choose the next number.

You see six numbers and have to pick the seventh. The patterns range from simple counting-up to squares, primes, triangular numbers and Fibonacci-style sums, and each answer explains the rule.

Start by checking the gaps between numbers. If the gaps are constant it is an arithmetic sequence. If the numbers multiply by the same amount each time it is geometric. If the gaps themselves grow, think squares or triangular numbers.

When nothing fits, look at pairs of neighbours: if each number is the sum of the two before it, you have a Fibonacci-style sequence. After you answer, the rule is shown so you can learn the patterns.

Frequently asked questions

How do I find the pattern?

Look at the differences between neighbouring numbers, then at ratios, then check for squares or primes.

Are the sequences always different?

They are generated from a set of rules with random starting values, so you will see many different ones.

What are triangular numbers?

Numbers like 1, 3, 6, 10, 15 formed by adding 1, then 2, then 3 and so on.