Chhattisgarh Board Solutions for Exercise 7: Exercise – 2

Find the arithmetic mean of $\frac{1}{2}$ and $-\frac{1}{2}$.

Find the value of $k$ if the arithmetic mean of $x^2+3xy$ and $y^2-3xy$ is $\frac{x^k+y^k}{2}$

Arithmetic mean and product of two numbers are $7$ and $45$ respectively. Find the numbers.

Arithmetic mean and sum of squares of two numbers are $6$ and $90$. Find the numbers.

Form an AP by inserting $6$ terms between $-4$ and $10$.

Form an AP by inserting $5$ terms between $11$ and $-7$.

If in an arithmetic progression the mean of $p^{\mathrm{th}}$ and $q^{\mathrm{th}}$ term is equal to mean of $r^{\mathrm{th}}$ and $s^{\mathrm{th}}$ term then prove that $p+q=r+s$.

$n$ terms lie between $7$ and $49$ in an AP. If ratio of the third term and the $n^{\mathrm{th}}$ term is $4:5$, then find the value of $n$.