$(1^{2}+2^{2}+3^{2}+\cdots+10^{2})$ is equal to:

Five numbers are in $A.P.$,whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$,then the greatest number amongst them is

The ratio of the sum of $m$ and $n$ terms of an $A.P.$ is $m^2 : n^2$. Then the ratio of the $m^{th}$ and $n^{th}$ term will be:

The first term of a harmonic progression is $1/7$ and the second term is $1/9$. The $12^{th}$ term is

Let $a_1, a_2, ......., a_{30}$ be an $A.P.$,$S = \sum_{i=1}^{30} a_i$ and $T = \sum_{i=1}^{15} a_{2i-1}$. If $a_5 = 27$ and $S - 2T = 75$,then $a_{10}$ is equal to

Let ${S_n} = \frac{1}{{{1^3}}} + \frac{{1 + 2}}{{{1^3} + {2^3}}} + \frac{{1 + 2 + 3}}{{{1^3} + {2^3} + {3^3}}} + \dots + \frac{{1 + 2 + \dots + n}}{{{1^3} + {2^3} + \dots + {n^3}}}$. If $100 S_n = n$,then $n$ is equal to: