List of top Mathematics Questions on Geometric Progression asked in KEAM

If $ a, a r, a r^2 $ are in a geometric progression (G.P.), then find the value of: $ \left| a \quad a r \right| \quad \left| a r^2 \quad a r^3 \right| = \left| a r^3 \quad a r^6 \right| $
The product of the first five terms of a GP is 32. What is the 3rd term?
The sum of the first 20 terms of the G.P. \( \sqrt{3} + \frac{-1}{\sqrt{3}} + \frac{1}{3\sqrt{3}} + \cdots \) is equal to
Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 
The first term of a G.P. is 3 and the common ratio is 2. Then the sum of first eight terms of the G.P. is
If the first term of a G.P. is 1 and the sum of 3rd and 5th terms is 90, then the positive common ratio of the G.P. is
If \( 1, a, b, c, 16 \) is in G.P., then \( \sqrt[3]{abc} = \)