14, 18, 23, 28, 34, 42, 50, 59, what next?

Question

Find the next term of 14, 18, 23, 28, 34, 42, 50, 59, ? The differences (4, 5, 5, 6, 8, 8, 9) almost form a pattern, but not quite. The sequence is not mathematical at all, and no formula will fit it; the question is really where these particular numbers come from.

Accepted Answer

The next term is 66. These are the street numbers of the stops on a Manhattan subway line running north: 14th Street, 18th, 23rd, 28th, 34th, 42nd, 50th, 59th, 66th, then 72nd, 79th, 86th, 96th. Why it fools people. The differences grow slowly and irregularly, which invites attempts at second differences and quadratic fits, none of which work. The numbers come from where the stations were built, and no formula reproduces that. The lesson. Not every sequence has a mathematical rule, and an interview may deliberately include one that does not, to see whether you recognise a dead end and ask "wh…

14, 18, 23, 28, 34, 42, 50, 59, what next?

Your answer

Discussion

Learn the concepts

Related questions