The $20^{th}$ term of the $A.P.$ $1, 11, 21, \ldots$ is........

The sum of the first $n$ even natural numbers is............

How many terms of the $A.P.$ $5, 8, 11, \dots$ add up to $670$?

For an $A.P.$,the sum of the $4^{th}$ term and the $8^{th}$ term is $24$,while the sum of the $6^{th}$ term and the $10^{th}$ term is $34$. Find the first term $a$ and the common difference $d$ of the $A.P.$

If the numbers $n-2, 4n-1$ and $5n+2$ are in $AP$,find the value of $n$.

Find the sum:
$\frac{a-b}{a+b}+\frac{3a-2b}{a+b}+\frac{5a-3b}{a+b}+\ldots$ to $11$ terms.