Geometric Progression

In the series 2, 6, 18, 54, ... what will be the 8th term ?

How many terms are there in the G.P. $3, 6, 12, 24,......,384$?

What should come in place of $?$ in the following number series?

$2 +4+8+\dots \dots$. How many terms of the series to make the sum equal to $1022$.

How many terms are there in the G.P.$3, 6, 12, 24, ... , 384 ?$

In the series $7, 14, 28, ...$, what will be the ${10}^{th}$ term ?

What should come in place of $?$ in the following number series?

If $2^{\frac{1}{c}}, 2^{\frac{b}{ac}}, 2^{\frac{1}{a}}$ are in $GP$, then which one of the following is correct?

If $1+\sin x+{\sin }^{2}x+{\sin }^{3}x+........+\infty$ is equal to $4+2\sqrt{3}, 0<x<\mathrm{\pi },$ then $x$ is equal to

CSK in the first $3$ overs of the game scored runs in geometric progression such that the runs scored in the first over are $5$ more than the runs scored in third over and 3$3$ more than the runs scored in the second over.

What is the total score of CSK at the end of $3$rd over $?$

Let $a_1,a_2,a_3,\dots$. be a G.P. of increasing positive numbers. Let the sum of its $6^{\text{th }}$ and $8^{\text{th }}$ terms be $2$ and the product of its $3^{\text{rd }}$ and $5^{\text{th }}$ terms be $\frac{1}{9}$. Then $6\left(a_2+a_4\right)\left(a_4+a_6\right)$ is equal to

If the sum of the series 

$\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{2^2}-\frac{1}{2·3}+\frac{1}{3^2}\right)+\left(\frac{1}{2^3}-\frac{1}{2^2·3}+\frac{1}{2·3^2}-\frac{1}{3^3}\right)+\left(\frac{1}{2^4}-\frac{1}{2^3·3}+\frac{1}{2^2·3^2}-\frac{1}{2·3^3}+\frac{1}{3^4}\right)+......$ is $\frac{\alpha }{\beta }$, where $\alpha$ and $\beta$ are co-prime, then $\alpha +3\beta$ is equal to ________. 

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

If $a,b,c \in R$ and $a^2+b^2+c^2=1$ then minimum and maximum value of $ab+bc+ca$ is

The value of $3^{\frac{1}{3}}{3}^{\frac{1}{9}}{3}^{\frac{1}{27}}.......\infty$ is

Find sum of $3+33+333+3333+....... \mathrm{up} \mathrm{to} \mathrm{n} \mathrm{terms}.$

The infinite GP series with first term $\frac{1}{4}$ and sum $\frac{1}{3}$ is

If $a^2+{\left(ar\right)}^2+{\left(a{r}^2\right)}^2=33033,\left(a,r\in N\right)$ then the value of $a+ar+a{r}^2$ is

If ${\left(21\right)}^{18}+20{\left(21\right)}^{17}+{\left(20\right)}^2{\left(21\right)}^{16}+.......+{20}^{18}=k\left({21}^{19}-{20}^{19}\right)$ then $k=$