The numbers in the pattern 1, 4, 10, 19, ___ increase by adding successive odd numbers. What is the next number?

Step-by-step solution

1. Compute successive differences: $4-1=3$, $10-4=6$, $19-10=9$.
2. Notice the differences are $3,6,9$, which increase by $3$ each time, i.e. successive odd multiples of $3$.
3. The next difference should be $12$ (next odd multiple of $3$).
4. Add this to the last term: $19+12=31$.
5. So the next number is $31$.

Concept tested: Recognise pattern of increasing odd differences

Published 10 October 2026 · How this solution was prepared and checked