Question 928744
*[tex \large a_3 = a_1 \cdot r^2] since you have a_1, the next term is a_1*r, third term is a_1*r^2.


*[tex \large 16 = 2r^2]
*[tex \large 8 = r^2]
*[tex \large r = \pm 2\sqrt{2}] <-- we don't know which one.

Then
*[tex \large a_6 = a_1 \cdot r^5 = 2r^5]


However the value of a6 depends on what r is. If *[tex \large r = 2\sqrt{2}] then *[tex \large a_6 = 2(2 \sqrt{2})^5 = 256 \sqrt{2}]. Otherwise *[tex \large a_6 = -256\sqrt{2}]. Impossible to determine what a_6 is without more info.