Question

How to find A1 in a geometric series for which sn= 105, r=-2 and n=6

Answer 1

Here we're discussing the "nth partial sum of a geom series."

                                                        1 - r^n
The formula for that is s(n) = a(1) --------------- 
                                                          1-r

We can subst. the given values and see where that takes us:

                   1 - (-2)^6        1 - 64
105 = a(1)*---------------- = ----------*a(1)  =  -21*a(1)
                     1-(-2)                3

                                               105
Solving this for a(1):  a(1) = --------- = -5    (answer)
                                               -21