"solve"? This word makes no sense.

"have the answer"? No, you don't. There are infinitely many answers. It is easily shown that there is an expression to produce all four of those answers, and again, infintely many others.

You must learn the concept of a "difference". It is a common expected method for such games.

Subtracting successive values from each other gives first differences.

3 - 1 = 2

13 - 3 = 10

39 - 13 = 26

89 - 39 = 50

Do it again to obtain the second differences

10 - 2 = 8

26 - 10 = 16

50 - 26 = 24

Do it again to obtain the third differences

16 - 8 = 8

24 - 16 = 8

From here, it is likely that you are supposed to assume ALL third difference are identical. This is actually quite a conceptual leap, given that we've only two of them.

Anyway, working backwards:

The next third difference = 8

The next second difference = 24 + 8 = 32

The next first difference = 50 + 32 = 82

The next value = 89 + 82 = 171

I'm not sure what this says about "the answer" that you have, but as long as your answer can be supported, it should be acceptable. 183, for example, might be the result of constant 5th differences of 12. It may be a bit silly, but it is supportable.

The next two values in the sequence I have defined are 293 and 463, oddly interspersed with your "answer" list.