If $a_m$ denotes the $m^{th}$ term of an $A.P.$,then $a_m$ =

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an Arithmetic Progression are $a$,$b$,and $c$ respectively,then $[a(q - r) + b(r - p) + c(p - q)] = ?$

If $\log 2, \log (2^n - 1)$ and $\log (2^n + 3)$ are in $A.P.$,then $n =$

Find the sum of all natural numbers lying between $100$ and $1000$ which are multiples of $5.$

For $p, q \in R$,consider the real-valued function $f(x) = (x - p)^2 - q$,where $x \in R$ and $q > 0$. Let $a_1, a_2, a_3, a_4$ be in an arithmetic progression with mean $p$ and a positive common difference $d$. If $|f(a_i)| = 500$ for all $i = 1, 2, 3, 4$,then the absolute difference between the roots of $f(x) = 0$ is:

If the sum of the first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms,then find the sum of the first $(p+q)$ terms.