Sequencing problem - Is it possible to solve this problem with the given information

Question

I have a sequencing problem that I cannot find a way to solve using the three major formulas for finding sequencing elements.

The difference between terms is given (1/2). The sum of the terms is minus 105/2, and the last term is also given (0).

However, neither the first term nor the number of terms is given.

I cannot find a way to solve such a problem. All of the formulas seem to require both the number and the first term and/or the last term.

The answers given are: Minus 7 for the first term, and 15 as the number of terms.

If this is solvable, I would very much appreciate the formula sequence.

If not, I would like to know that as well.

Thanks so much.

Ron

Answer 1

The last term of the sequence is a + (n-1)d...in this case

0 = a +(n-1)(1/2) => n= 1-2a

The sum of the series is (n/2)(a + l) where l is the last term...in this case

-105/2 = na/2 => n = -105/a

Therefore, -105/a = 1 - 2a

This gives you a quadratic which you can solve by formula to get a = -7. and then n = 15.