There are many possibilities

Could be this way:

51-8 = 5-8 = -3
52-8 = 25-8 = 17
53-8 = 125-8 = 117
54-8 = 625-8 = 617
...


------------------------------

Or it could be this way:

-3+20 = 17
17+100 = 117
117+180 = 297
297+260 = 557
...
where we add terms of the arithmetic sequence 20,100,280,260,...
to each term to get the next term.

And the general term is ak = 40k2-100k+57
 


But there are trillions of other sequences that have -3,17,117
for their first three terms.  So how on earth could your teacher
expect you or anybody to guess which one he or she had in mind??

Edwin