If ${\log _5}2,\,{\log _5}({2^x} - 3)$ and ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ are in $A.P.$ then the value of $x$ is :-
$0$
$-1$
$3$
$4$
If the sum of $n$ terms of an $A.P$. is $2{n^2} + 5n$, then the ${n^{th}}$ term will be
If ${S_1},\;{S_2},\;{S_3},...........{S_m}$ are the sums of $n$ terms of $m$ $A.P.'s$ whose first terms are $1,\;2,\;3,\;...............,m$ and common differences are $1,\;3,\;5,\;...........2m - 1$ respectively, then ${S_1} + {S_2} + {S_3} + .......{S_m} = $
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................
Which of the following sequence is an arithmetic sequence