A series whose $n^{th}$ term is $\left( {\frac{n}{x}} \right) + y,$ the sum of $r$ terms will be
$\left\{ {\frac{{r(r + 1)}}{{2x}}} \right\} + ry$
$\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\}$
$\left\{ {\frac{{r(r - 1)}}{{2x}}} \right\} - ry$
$\left\{ {\frac{{r(r + 1)}}{{2y}}} \right\} - rx$
Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$
If the numbers $a,\;b,\;c,\;d,\;e$ form an $A.P.$, then the value of $a - 4b + 6c - 4d + e$ is
If ${S_k}$ denotes the sum of first $k$ terms of an arithmetic progression whose first term and common difference are $a$ and $d$ respectively, then ${S_{kn}}/{S_n}$ be independent of $n$ if
The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots,$ $b_{ m }$ is $2$ more than the common difference of $A.P.$ $a _{1}, a _{2}, \ldots, a _{ n } .$ If $a _{40}=-159, a _{100}=-399$ and $b _{100}= a _{70},$ then $b _{1}$ is equal to
If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be