Question 1094808
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2, 4 and 8.   


Another progression is 8, 4, 2.


Mental solution.  3 seconds.



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If you want algebra solution, here it is.


<pre>
Let "a" be the first term and "r" be the common ratio.


Then the terms are  a, ar and ar^2.


a + ar + ar^2 = 14,     (1)
a * ar * ar^2 = 64      (2)


From (2) you have  a^3*r^3 = 64  ====>  (ar)^3 = 64 ===>  ar = {{{root(3,64)}}} = 4.


Next step substitute ar = 4 everywhere into (1). You will get

a + 4 + 4r = 14,   or

a + 4r = 10.


Express a = 10-4r  and substitute it into ar = 4.


You will get a quadratic equation

(10-4r)*r = 4.


The rest is just arithmetic.
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