EXERCISE 9.2

Find the sum of odd integers from $1$ to $2001$.

The ratio of the sums of $m$ and $n$ terms of an A.P. is $m^2:n^2$. Show that the ratio of $m^{th}$ and $n^{th}$ term is $(2m-1):(2n-1)$.

If the sum of $n$ terms of an A.P. is $3n^2+5n$ and its $m^{th}$ term is $164,$ find the value of $m.$

Insert five numbers between $8$ and $26$ such that the resulting sequence is an A. P.

If $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the A.M. between $a$ and $b$, then find the value of $n.$

Between $1$ and $31$, $m$ numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of $7^{th}$ and $(m-1{)}^{th}$ numbers is $5:9.$ Find the value of $m.$

A man starts repaying a loan as first installment of$₹100$. If he increases the installment by $₹5$ every month, what amount he will pay in the $30^{th}$ installment?

The difference between any two consecutive interior angles of a polygon is $5°$. If the smallest angle is $120°$, find the number of the sides of the polygon.