If $n$ be odd or even, then the sum of $n$ terms of the series $1 – 2 + $ $3 – $$4 + 5 – 6 + ……$ will be

If the sum of $n$ terms of an $A.P.$ is $\left(p n+q n^{2}\right),$ where $p$ and $q$ are constants, find the common difference.

Let $a$, $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x ^{2}-8 ax +2 a =0$ and $q$ and $s$ are the roots of the equation $x^{2}+12 b x+6 b$ $=0$, such that $\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }$ are in A.P., then $a ^{-1}- b ^{-1}$ is equal to $……$

If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a – c)}^2}}}{{({b^2} – ac)}} = $

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=n \frac{n^{2}+5}{4}$