If ${A_1},\,{A_2}$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{{24}}$ , then their values are
$\frac{7}{{72}},\,\frac{5}{{36}}$
$\frac{{17}}{{72}},\,\frac{5}{{36}}$
$\frac{7}{{36}},\,\frac{5}{{72}}$
$\frac{5}{{72}},\,\frac{{17}}{{72}}$
Let $x_n, y_n, z_n, w_n$ denotes $n^{th}$ terms of four different arithmatic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20,$ then maximum value of $x_{20}.y_{20}.z_{20}.w_{20}$ is-
$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be
Consider a sequence whose sum of first $n$ -terms is given by $S_n = 4n^2 + 6n, n \in N$, then $T_{15}$ of this sequence is -
If $f(x + y,x - y) = xy\,,$ then the arithmetic mean of $f(x,y)$ and $f(y,x)$ is
If ${a_1},\;{a_2},............,{a_n}$ are in $A.P.$ with common difference , $d$, then the sum of the following series is $\sin d(\cos {\rm{ec}}\,{a_1}.co{\rm{sec}}\,{a_2} + {\rm{cosec}}\,{a_2}.{\rm{cosec}}\,{a_3} + ...........$$ + {\rm{cosec}}\;{a_{n - 1}}{\rm{cosec}}\;{a_n})$