For a given $A.P.$,$a=2$ and $d=3$. Then,$S_{30} = \dots$

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

For the $A.P.$ $0, \frac{1}{2}, 1, \frac{3}{2}, \ldots,$ the common difference is $\ldots \ldots \ldots \ldots$

The first term of an $AP$ is $-5$ and the last term is $45$. If the sum of the terms of the $AP$ is $120$,then find the number of terms and the common difference.

The sum of three numbers in $A.P.$ is $21$. The product of the first and the third number exceeds the second number by $6$. Find those numbers.

$A$ person saved $Rs. 16,500$ in all during $10$ years. After the first year,every year he saved $Rs. 100$ more than what he had saved the previous year. Find his savings of the first year.