Number series: find the next number
Number series show up in cognitive aptitude tests and logical reasoning sections. You see four to six numbers and pick, or type, the next one. A short routine finds most rules:
- Find the differences between neighbors. If they're all the same, the series adds or subtracts a fixed amount.
- If the differences change, find their differences. 2, 5, 10, 17, 26 has differences 3, 5, 7, 9, rising by 2, so the next is 26 + 11 = 37.
- If the numbers grow fast, try ratios. 3, 6, 12, 24 doubles each time.
- If the numbers zig-zag, split the series. 4, 20, 6, 18, 8, 16 is two series: 4, 6, 8 and 20, 18, 16.
- Look for squares, cubes and sums. 1, 4, 9, 16 are squares; in 2, 3, 5, 8, 13 each number adds the two before it.
Check your rule against every step, not just the last one.
Series: 3, 4, 7, 12, 19, ?
Differences: 1, 3, 5, 7
Next difference: 9
Answer: 19 + 9 = 28
Write the differences under the series. The pattern is often in the second row.