If $\log _{10} 2, \log _{10} (2^x + 1), \log _{10} (2^x + 3)$ are in $A.P.,$ then :-
$x = 0$
$x = 1$
$x = \log _{10} 2$
$x = \frac{1}{2} \log _2 5$
If $19^{th}$ terms of non -zero $A.P.$ is zero, then its ($49^{th}$ term) : ($29^{th}$ term) is
Let $a_1=8, a_2, a_3, \ldots a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is
If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $
If $1,\,\,{\log _9}({3^{1 - x}} + 2),\,\,{\log _3}({4.3^x} - 1)$ are in $A.P.$ then $x$ equals
Show that the sum of $(m+n)^{ th }$ and $(m-n)^{ th }$ terms of an $A.P.$ is equal to twice the $m^{\text {th }}$ term.