.
2, 4 and 8.
Another progression is 8, 4, 2.
Mental solution. 3 seconds.
-----------
If you want algebra solution, here it is.
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 = = 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.