If the sum of the first four terms of an $A.P.$ is $6$ and the sum of its first six terms is $4$, then the sum of its first twelve terms is

$a_1, a_2, a_3, \dots, a_{100}$ are in an arithmetic progression,where $a_1 = 3$ and $S_p = \sum_{i=1}^p a_i, 1 \le p \le 100$. For any integer $n$,let $m = 5n$. If $S_m/S_n$ is independent of $n$,then $a_2 = \dots$

If $p$ times the $p^{th}$ term of an arithmetic progression is equal to $q$ times its $q^{th}$ term,then the $(p + q)^{th}$ term of this progression is........

If the sum of the first $n$ terms of an $A.P.$ is $c n^2$,then the sum of the squares of these $n$ terms is

The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

The income of a person is $Rs. \,3,00,000$ in the first year and he receives an increase of $Rs. \,10,000$ to his income per year for the next $19$ years. Find the total amount he received in $20$ years.