List of top Mathematics Questions on geometric progression

If \( 1 + \sin\theta + \sin^2\theta + \dots \text{ upto } \infty = 2\sqrt{3} + 4 \), then \( \theta = \)

Consider an infinite series with first term a and common ratio r. If its sum is 4 and the second term is \(\frac{3}{4}\), then

If the roots of the equation $x^3 - 7x^2 + 14x - 8 = 0$ are in geometric progression, then the common ratio can be:

Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:

The number of terms in the sequence $2, 6, 18, \ldots, 1458$ is:

The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the common ratio is

Let $t_1, t_2, t_3, \ldots, t_{2n}$ be in G.P. with common ratio $r$. Then:

If $\dfrac{4^{n+1} + 16^{n+1}}{4^n + 16^n}$ is the Geometric Mean between $4$ and $16$, then the value of $n$ is:

If \( A = 1 + r^a + r^{2a} + r^{3a} + \cdots \infty \) and \( B = 1 + r^b + r^{2b} + r^{3b} + \cdots \infty \), then \( a/b \) is equal to

The sum of the geometric series \(\sqrt{3}+\sqrt{12}+\sqrt{48}+\dots\) up to \(10\) terms is

If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to

If the numbers \( x, 6, y, 54, 162 \) are in geometric progression, then \( \dfrac{y}{x} \) is equal to

Let $G_1, G_2, G_3$ be geometric means between $l$ and $n$, where $l$ and $n$ are positive real numbers. Then the common ratio is

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is

The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:

The 25th term of $9, 3, 1, \frac{1}{3}, \frac{1}{9}, \ldots$ is:

The product of first 5 terms of a G.P., whose terms are increasing, is 32. The third term of the G.P. is

Let \( a_1, a_2, a_3, \ldots \) be in G.P. If \( a_1 \cdot a_2 \cdot a_3 = 64 \) and \( a_1 \cdot a_2 \cdot a_3 \cdot a_4 \cdot a_5 = 32 \), then common ratio is

In a G.P., the first and third terms are 4 and 8 respectively. Then the \(21^{\text{st}}\) term is

A geometric progression consists of an even number of termsIf the sum of all the terms is five times the sum of the terms occupying the odd places, then the common ratio of the geometric progression is

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is 4, and the difference between third and fifth term is \( \frac{32}{81} \), then which of the following is not true?

\(a_{1}, a_{2}, \ldots , a_{10}\) are in G.P., and if \(a_{1} + a_{2} = 6, a_{9} + a_{10} = \frac{3}{128}\) then the common ratio of the G.P. is equal to

Let \(a_{n} = 2^{n - 1}, n = 1, 2, 3, \ldots\) . Then the value of the sum \(\sum_{n = 1}^{20} a_{n}\) is equal to

Three numbers a, b, and c are in G.P. If abc = 27 and a + c = 10, then a² + b² + c² =

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to