9514 1404 393
Answer:
Either of ...
- {-20, -100, -500, -2500, -12500}
- {20, -100, 500, -2500, 12500}
Explanation:
For some common ratio r, the first of the "geometric means" will be -4r, the next will be -4r^2, and so on. The 5th will be -4r^5, and finally, -62500 will be -4r^6.
Solving this last relation for r gives ...
-4r^6 = -62500
r^6 = 15625
Then r can be either of ...
r = ±15625^(1/6) = ±5
For r = 5, the means are ...
-4·5 = -20, and -100, -500, -2500, -12500
For r = -5, the means are ...
-4(-5) = 20, and -100, 500, -2500, 12500