If the ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ term of an arithmetic sequence are $a , b$ and $c$ respectively, then the value of $[a(q - r)$ + $b(r - p)$ $ + c(p - q)] = $
$1$
$- 1$
$0$
$1/2$
If the sum of $n$ terms of an $A.P.$ is $nA + {n^2}B$, where $A,B$ are constants, then its common difference will be
If $\log _{10} 2, \log _{10} (2^x + 1), \log _{10} (2^x + 3)$ are in $A.P.,$ then :-
The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is
The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1},\;{S_2},\;{S_3}$ respectively. The true relation is
The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is