List of top Mathematics Questions on Geometric Progression

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

Which of the following is not in Geometric Progression?

If \(x-1,\ x+2\) and \(x+8\) are three consecutive terms of a Geometric Progression, then the value of \(x\) 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 three geometric means between 4 and 324 are

The $3^{\text{rd}}$ and $6^{\text{th}}$ terms of a G.P. are, respectively 108 and -32. Then the first term is

The sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the 1st term, the common ratio, and the sum to \( n \) terms of the G.P.

The 4th term of a G.P. is square of its second term, and the 1st term is -3. Determine its 7th term.

If \( a_1, a_2, a_3, \ldots \) are in increasing geometric progression such that \[ a_1 + a_3 + a_5 = 21, a_1 a_3 a_5 = 64, \] then \( a_1 + a_2 + a_3 \) is:

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 ________.

In a Geometric Progression (G.P.), if the third term is 4, then the product of the first 5 terms is

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| $

Find the sum of the infinite geometric series: $$ S = 8 + 4 + 2 + \cdots $$ if it converges.

Let \( a, ar, ar^2, \dots \) be an infinite G.P. If $$ \sum_{n=0}^\infty ar^n = 57 \quad \text{and} \quad \sum_{n=0}^\infty a^3 r^{3n} = 9747, $$ then \( a + 18r \) is equal to: