if the third and ninth term of a geometric series with a positive common ratio are -3 and -192 respectively, determine the value of the first term, "a".
The multiplier factor for successive terms is (192/3)^1/6 = 64^1/6 = +2 or -2
The third term would have the same sign as the first term, and be 1/4 as large.
Thus a1 must be negative.
The series is
-3/4, -3/2, -3, -6, -12, 24, -48, -96, -192
or
-3/4, 3/2, -3, 6, -12, 24, -48, 96, -192
In either case, the first term is -3/4.