Question

Insert 5 geometric means between -4 and -62 500​

Answer 1

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