For the $A.P.$ $100, 98, 96, 94, \ldots$,find the value of $a$.

In the $AP: 10, 5, 0, -5, \ldots$,the common difference $d$ is equal to $5$. Justify whether the above statement is true or false.

Which term of the $A.P.$ $85, 78, 71, \ldots$ is its first negative term? If the order of this term is $n$,find $S_{n}$.

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

If the $9^{\text{th}}$ term of an $AP$ is zero,prove that its $29^{\text{th}}$ term is twice its $19^{\text{th}}$ term.

$A$ 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.