If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

If the $4^{th}, 7^{th}$ and $10^{th}$ terms of a $G.P.$ are $a, b, c$ respectively,then the relation between $a, b, c$ is

In an increasing geometric progression of positive terms,the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text{th}}$,$6^{\text{th}}$,and $8^{\text{th}}$ terms is:

Let $n (> 1)$ be a positive integer. The largest integer $m$ such that $(n^m + 1)$ divides $(1 + n + n^2 + \dots + n^{127})$ is:

The number of bacteria in a certain culture doubles every hour. If there were $30$ bacteria present in the culture originally,how many bacteria will be present at the end of $2^{\text{nd}}$ hour,$4^{\text{th}}$ hour and $n^{\text{th}}$ hour?

If the sum of an infinite $GP$ is $9$ and the sum of the first two terms is $5$,then their common ratio is .....