If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times of its $21^{st}$ term, then its $25^{th}$ term is equal to
$24$
$120$
$0$
None of these
If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $
If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of last and first term is $273$, then the numbers are
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be
If $\log 2,\;\log ({2^n} - 1)$ and $\log ({2^n} + 3)$ are in $A.P.$, then $n =$