A.M. and G.M.

For what value of $n$, $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the arithmatic mean of $a$ and $b$.

If the arithmetic mean of two numbers is $5$ and the geometric mean is $4$, then the numbers are:

What is the minimum value of the expression $x^2 +\frac{1}{x^2+1}-3$?

Sudhir is travelling from Patna to Dehradun. For half of the time, his speed is $\mathrm{x} \mathrm{kmph}$, and for other half of the time, his speed is $\mathrm{y} \mathrm{kmph}$. During return journey, for half of the distance, his speed is $\mathrm{x} \mathrm{kmph},$ and for other half of the distance, his speed is $\mathrm{y} \mathrm{kmph}$. If $\mathrm{x}\ne$ $\mathrm{y}$, then which of the following is definitely correct?

The sum of natural numbers upto $200$excluding those divisible by$5$ is _____.

If $a, b, c$ are in $\mathrm{A}.\mathrm{P}.$ as well as in $\mathrm{G}.\mathrm{P}.$ then ______.

The $\mathrm{A}.\mathrm{M}.$of two positive numbers is $40$and their $\mathrm{G}.\mathrm{M}.$is $24$. The numbers are _____.

Which of the following statements is correct:

If $a, b, c$ be in A.P. and $a^2, b^2, c^2$ are in H.P.

Which among the following is Arithmetico-geometric Progression?

$\mathrm{I}. \left(10·8\right)+\left(20·8^2\right)+\left(30·8^3\right)+\left(40·8^4\right)+\_\_\_\_$

$\mathrm{II}. \left(10·8\right)+\left(20·8^2\right)+\left(30·8^3\right)+\left(50·8^4\right)+\_\_\_\_$

$\mathrm{III}. \left(10·8\right)+\left(20·9^2\right)+\left(30·8^3\right)+\left(40·{18}^4\right)+\_\_\_\_$

$\mathrm{IV}. \left(10·8\right)+\left(25·8^2\right)+\left(30·8^3\right)+\left(45·8^4\right)+\_\_\_\_$

Find the sum of $1+\frac{3}{3}+\frac{5}{3^2}+\frac{7}{3^3}...............\infty$:

Find the Geometric Mean : $5, 16, 125, 81$

If the mean of numbers $28, \mathrm{x}, 42, 78$ and $104$ is $62$, what is the mean of $48, 62, 98, 124$ and $\mathrm{x}$?

If the arithmetic mean of $14$ observations $26, 12, 14, 15, \mathrm{x}, 17, 9, 11, 18, 16, 28, 20, 22, 8$ is $17$. Find the missing observation.

Find the G.M. of the following values: $10$, $25$, $5$, and $30$

The mean of a data set with $12$ observations is calculated as $19.25$. If one more value is included in the data, then for the new data with $13$ observations, mean becomes $20.$ Value of this ${13}^{\mathrm{th}}$ observation is​

The average height of six boys is $152$ centimetres tall. How tall is the sixth boy if the five boys' heights are $151 \mathrm{cm}$, $153 \mathrm{cm}$, $155 \mathrm{cm}$, and $149 \mathrm{cm}$, respectively?

Suppose the mean of five observations. $\mathrm{x}$ , $\mathrm{x} + 4$, $\mathrm{x} + 6$, $\mathrm{x} + 8$  and  $\mathrm{x} + 12$ is $16$, find the value of $\mathrm{x}$.

Find the value of $\mathrm{x}$ if the mean of $9, 8, 10, \mathrm{x},$ and $12$ is $15$.

The mean of $100$ items was $46$ . Later it was found that an item $43$ was misread as $34$ and a second item $16$ was misread as $61$. It was also found that the number of items was $90$ instead of $100$. Then the correct mean must be

If first five prime numbers are given, then find their arithmetic mean?