Question

What is the next term of this sequence : `1,3,5,8,11,15,19,24...` ?

Answer 1

The next number in the sequence should be `29`

The sequence is `+2, +2, +3, +3, +4, +4, +5` so the next term should also be: `t_(n + 1) = t_n + 5` Or `t_(n + 1) = 24 + 5 = 29`

Answer 2

`29` or `30` or anything you like.

Explanation:

Given a finite number of terms of an infinite sequence does not determine the remainder of the sequence, unless you are given extra information about the sequence, e.g. that it is arithmetic, geometric, etc. Without such information the sequence could have any values as its continuation.

That said, if the sequence matches an obvious pattern, then that is probably a good guess concerning the intention of the writer.

Given:

`1, 3, 5, 8, 11, 15, 19, 24`

Let us look at the sequence of differences between consecutive terms:

`2, 2, 3, 3, 4, 4, 5`

So if the sequence of differences continues in similar fashion, we would probably expect it to continue:

`2, 2, 3, 3, 4, 4, 5, color(red)(5), color(red)(6), color(red)(6), color(red)(7),...`

In which case our given sequence would continue:

`1, 3, 5, 8, 11, 15, 19, 24, color(red)(29), color(red)(35), color(red)(41), color(red)(48),...`

This sequence is listed in the online encyclopedia of integer sequences as A024206. There are 5 other matches for the given sequence, all but one of which have `29` as the next term. The exception has `30` instead.