Fuse is currently one the most flawed but challenging games out there. Not only do you have to solve for the mathematical progression, but you have to test if your solution is the most likely solution that will be accepted, because about 5% of the games have more than one solution and Lumosity will only accept one (they are working that issue and hope to get to a point there each Fuse only has one solution). So it is best to try to figure out the common types of mathematical progressions that the game designers are using to design the game (keep track of those generalized progressions) as those will derive, most often, the answer Lumosity wants.

So try the following first, where i is an increment that can change by a constant amount, for example {3, 1, -1, ...}, x is the first number in the series, y is the second number, and b is a factor, typically {-3, -2, 2, 3}: (1) x+y+i, (2) x-y+i, (3) y -x+i, (4) ba+i (5) b(a+i), (6) b(a-b). Also sometimes, add the number that is most similar to the last number next to it and see if you can figure out how that number would work into a progression and then work backwards.

P.S. Some solutions will make you smile. The game designers are obviously using semi-complex series to derive each Fuse. But sometimes that complexity can be simplified into something hilarious that the designers missed. One solution was explained by a complex mathematical progression but simplified into the following answer 3, 4, 5, 6, 7, 8, 9.