Answers

2016-07-04T22:45:16+08:00
It should be 64.
If we let x be the first term, y be the second term, and r be the common ratio (that number which we multiply to x to get y, and also the number we multiply to y to get 4, which is the third term), then we get
 \sqrt{xy}=32\\xy = 32^2
We also know that xr = y \\ \text{and}\\yr = 4


We now have a system of three equations, and three unknowns.
Solving for r gives us \frac{y}{x} = r = \frac4y\\x = \frac{y^2}4
Substituting this in the first equation for x gives
 \frac{y^3}{4}=32^2
Which, when solved, gives y=16

Thus, since yr = 4, we can deduce that r = \frac14
Finally, since xr = y, then xr = 16, and \frac14x = 16\\x = 64
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