List of top Mathematics Questions on geometric progression

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
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
Let a1, a2, a3, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a1 a9+a2 a4 a9+a5+a7 is equal to __________.

Let \( 0 < z < y < x \) be three real numbers such that \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in an arithmetic progression and \( x, \sqrt{2}y, z \) are in a geometric progression. If \( xy + yz + zx = \frac{3}{\sqrt{2}} xyz \), then \( 3(x + y + z)^2 \) is equal to ____________.

If sum of four numbers in GP is 60 and AM of first and last is 18, then the numbers are: