Geometric Progression

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

Find the sum of the following series:

$\left(2+2^2+2^3+........+2^9\right)=?$

The sum of the first $10$ terms of the series $\sqrt{2}+\sqrt{4}+\sqrt{8}+............$ is equal to_____.

If $1 + 10 + {10}^2 + .............$ upto $n$ terms$=\frac{{10}^n-1}{9}$, then the sum of the series $4 + 44 + 444 + .........$ upto $n$ term is _____.

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?

Three numbers is $\mathrm{G}.\mathrm{P}.$ with their sum is $130$ and their product is $27,000$ are _________

In the sequence $25,5,1,\dots ,\frac{1}{3125}$ which term is $\frac{1}{3125}$?

Direction Each of the following questions is followed by two statements:

What is the middle number of $7$consecutive whole numbers?

$\left(\mathrm{I}\right)$ Product of number is $702,800$ .

$\left(\mathrm{II}\right)$ Sum of the number is $105$ .

Given $\mathrm{A}=2^{65}$ and $\mathrm{B}=\left(2^{64}+2^{63}+2^{62}+\dots +2°\right)$, which of the following is true?

If $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\cdots$ upto $\infty =\frac{{\mathrm{\pi }}^2}{6}$, then value of $\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\cdots$ upto $\infty$ is

The numbers $x, 8, y$ are in $\mathrm{G}.\mathrm{P}.$and the numbers $x, y,-8$ are in $\mathrm{A}.\mathrm{P}.$The values of $x, y$ are _______.

If the continued product of three numbers in $\mathrm{G}.\mathrm{P}.$ is $27$and the sum of their products in pairs is $39$the numbers are_____________

Find five numbers in $\mathrm{G}.\mathrm{P}.$ such that their product is $32$and the product of the last two is $108$.

Three numbers in $\mathrm{G}.\mathrm{P}$. with their sum $\frac{13}{3}$and sum of their squares $\frac{91}{9}$ are

Three numbers in $\mathrm{G}.\mathrm{P}$. with their sum $130$and their product $27,000$are__________