What rule governs the sequence 3, 9, 27, 30, 33?

Question

I recently had to complete an assessment for a job application which dealt with recognizing the patterns in number sequences and identifying what the next number in the sequence would be. One sequence which certainly stumped me was:

3, 9, 27, 30, 33

Now looking at it I believe the next number would be 51. I got that from there being a difference of 6 between 3 and 9, then a difference of 18 from 9 to 27, then a combined difference of 6 from 27 to 33. So the pattern, I think, is a difference of 6 (which can be done in one step or multiple) followed by a jump of 18. I now think to add 18 to the 33 to get the next number as 51. However I am not sure, and want to see what others think. I would be interested in all thoughts and opinions. Thank you in advance.

Answer 1

Ignoring the first two terms, which are clearly observational errors, each term is 3 more than their predecessor.

Answer 2

I think the only sensible answer to this (kind of) question in a job interview is "it depends". There is not enough information even to make a probable guess.

And any guess (for example, for the sequence $2,4,6,8, \ldots$) is only probable. Absent further information there are infinitely many ways to continue any finite sequence.

See Is there a way of making "guess the next number in the sequence" rigorous? .