Let ${a_1},{a_2},{a_3}, \ldots $ be terms of $A.P.$ If $\frac{{{a_1} + {a_2} + \ldots + {a_p}}}{{{a_1} + {a_2} + \ldots + {a_q}}} = \frac{{{p^2}}}{{{q^2}}},p \ne q$ then $\frac{{{a_6}}}{{{a_{21}}}}$ equals
$\frac{{41}}{{11}}$
$\frac{7}{2}$
$\frac{2}{7}$
$\frac{{11}}{{41}}$
If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......
Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $
Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$
For any three positive real numbers $a,b,c$ ; $9\left( {25{a^2} + {b^2}} \right) + 25\left( {{c^2} - 3ac} \right) = 15b\left( {3a + c} \right)$ then
Let $S_n$ and $s_n$ deontes the sum of first $n$ terms of two different $A.P$. for which $\frac{{{s_n}}}{{{S_n}}} = \frac{{3n - 13}}{{7n + 13}}$ then $\frac{{{s_n}}}{{{S_{2n}}}}$