If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =
$\frac{2}{{{a_{m + k}} + {a_{m - k}}}}$
$\frac{{{a_{m + k}} - {a_{m - k}}}}{2}$
$\frac{{{a_{m + k}} + {a_{m - k}}}}{2}$
None of these
Let $a_1, a_2, \ldots \ldots, a_n$ be in A.P. If $a_5=2 a_3$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots . \cdot \frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to $..........$.
If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then
If $1, \log _{10}\left(4^{x}-2\right)$ and $\log _{10}\left(4^{x}+\frac{18}{5}\right)$ are in
arithmetic progression for a real number $x$ then the value of the determinant $\left|\begin{array}{ccc}2\left(x-\frac{1}{2}\right) & x-1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0\end{array}\right|$ is equal to ...... .
If the roots of the equation ${x^3} - 12{x^2} + 39x - 28 = 0$ are in $A.P.$, then their common difference will be
If ${S_n}$ denotes the sum of $n$ terms of an arithmetic progression, then the value of $({S_{2n}} - {S_n})$ is equal to