List of top Mathematics Questions on Geometric Progression asked in KEAM

If $\cos \theta, \sqrt{2}\sin \theta$ and $\sqrt{3}\tan \theta$, where $0 < \theta < \frac{\pi}{2}$, are the second, third and fourth terms of a geometric series, respectively, then the first term of the geometric series is
The sum of four consecutive terms in a geometric progression is 960. If the fourth term is 8 times as large as the first term, then the smallest number in the geometric progression is
The sum of the first two terms of a geometric series is 12 and the third term is 16. Then the common ratio $r > 0$ of the geometric progression is
The first and the twentieth terms of a G.P. are 512 and \(\frac{1}{1024}\) respectively. Then the common ratio is
If \(k\), 6 and \(k+5\) are the first three terms of a geometric series, then the possible values of the common ratio are
A geometric series has common ratio \(\frac{1}{3}\). If the sum of first four terms is 200, then the first term is
The sum of the second and third terms of a G.P. is 8 and the fourth term is 4. The common ratio \(r \neq 1\) is
If the $3^{\text{rd}}$, $7^{\text{th}}$, $11^{\text{th}}$ terms of a geometric progression are $a$, $b$, $c$ respectively, then $(ac)^{4} =$
If $a, x, y, b$ are in G.P., then $(x+y)^{2}=$
The $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P. are, respectively 108 and -32. Then the first term is
The three geometric means between 4 and 324 are
Let $a, \frac{3}{4}, ar^{2}, ar^{3}, \dots$ be in G.P. where $r>0$. If the product of the first four terms is $\frac{3^{6}}{4^{5}}$, then $a$ is equal to ________.
The product of the first five terms of a GP is 32. What is the 3rd term?
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 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 the second and fifth terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is:
If the second and fifth terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is:
If the second and fifth terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is:
If \( 1, a, b, c, 16 \) is in G.P., then \( \sqrt[3]{abc} = \)