Aseries contains 18 numbers and has a sum of 4,185. the last number of the series is 275. what is the first number?

I'll assume the sequence is arithmetic just because that would involve less work (and in fact, if the series is geometric, there is more than one solution).

So the sequence takes the form , where is the common difference between successive terms. You can solve this recursively to find an explicit solution for in terms of the first term in the sequence, namely



Now, the summation of the first terms of the sequence amounts to



The last sum can be computed using the formula



so you end up with



Meanwhile, you know the last term in the series is , so you end up with another equation



You have enough information to solve for and, more importantly, . You should get (and the common difference turns out to be ).