The sum of the first $20$ terms common between the series $3 + 7 + 11 + 15 + \dots$ and $1 + 6 + 11 + 16 + \dots$ is

$A$ person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{th}$ minute. If $a_1 = a_2 = \ldots = a_{10} = 150$ and $a_{10}, a_{11}, \ldots$ are in an $A.P.$ with common difference $-2$,then the time taken by him to count all notes is ............... $minutes$.

If $a, b, c$ are in $A.P.$,then $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$ will be in

Let $a_n$ be the $n^{\text{th}}$ term of an $A.P.$ If $S_n = a_1 + a_2 + a_3 + \dots + a_n = 700$,$a_6 = 7$,and $S_7 = 7$,then $a_n$ is equal to:

If $a, b, c, d, e, f$ are in $A.P.$,then the value of $e - c$ is

If the $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$,then its $n^{th}$ term is: