Recent questions tagged geometric-progression

Let the $\text{m-th}$ and $\text{n-th}$ terms of a geometric progression be $\dfrac{3}{4}$ and $12,$ respectively, where $\text{m < n}.$ If the common ratio of the progr...

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ...

An infinite geometric progression $a_{1},a_{2},a_{3},\dots\dots$ has the property that $a_n =3(a_{n+1}+a_{n+2}+\dots\dots)$ for every $n\geq 1$. If the sum $a_{1}+a_{2}+a...

Suppose, $\log_{3}x= \log_{12}y= a$, where $x, y$ are positive numbers. If $\text{G}$ is the geometric mean of $x$ and $y$, and $\log_{6}\text{G}$ is equal to$\sqrt{a}$$2...

If $(a^{2}+b^{2}),(b^{2}+c^{2})$ and $(a^{2}+c^{2})$ are in geometric progression, which of the following holds true?$b^{2}-c^{2}= \dfrac{a^{4}-c^{4}}{b^{2}+a^{2}} \\$$b^...