If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then
${a^2}b,\,{c^2}a,\,{b^2}c$ are in $A.P.$
${a^2}b,\,{b^2}c,\,{c^2}a$ are in $H.P.$
${a^2}b,\,{b^2}c,\,{c^2}a$ are in $G.P.$
None of these
The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1},\;{S_2},\;{S_3}$ respectively. The true relation is
If $a _{1}, a _{2}, a _{3} \ldots$ and $b _{1}, b _{2}, b _{3} \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}$ then $a_{4} b_{4}$ is equal to
The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms
Let $\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},.....,$ $({x_i} \ne \,0\,for\,\,i\, = 1,2,....,n)$ be in $A.P.$ such that $x_1 = 4$ and $x_{21} = 20.$ If $n$ is the least positive integer for which $x_n > 50,$ then $\sum\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} $ is equal to.
The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is