The famous mathematician associated with finding the sum of the first $100$ natural numbers is

$A$ person has to clear a debt of $Rs. 3250$ by monthly instalments. In the first month he has to pay $Rs. 20$ and then onwards every instalment is $Rs. 15$ more than the previous instalment. How long will it take to clear the debt?

For a given $A.P.$,the $5^{th}$ term is $20$ and the $10^{th}$ term is $35$. Find the sum of the first $20$ terms of this $A.P.$

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

How many terms of the $A.P.$ $8, 15, 22, \ldots$ add up to $1490$?

For a given finite $A.P.$,$a=1, l=10$ and $n=10$. Then,$S_{10} = ........$