Find the $9^{\text{th}}$ term in the sequence whose $n^{\text{th}}$ term is given by $a_{n} = (-1)^{n-1} n^{3}$.

What is the sum of $n$ terms of the series $1 \cdot 3 \cdot 5 + 2 \cdot 5 \cdot 8 + 3 \cdot 7 \cdot 11 + \dots$?

$t_1, t_2, t_3, \ldots, t_{n}$ are positive integers,$S_{n} = t_1 + t_2 + t_3 + \ldots + t_{n}$. Given $S_1 = 1^2, S_2 = 3^2, S_3 = 6^2, S_4 = 10^2, S_5 = 15^2$. Following this pattern,if $S_{10} = k^2$,then $k =$

$\sum\limits_{r = 1}^n {\sum\limits_{m = 1}^r {m} } = \dots$

The sum,$\sum_{n=1}^{7} \frac{n(n+1)(2n+1)}{4}$ is equal to

For a series whose $n^{th}$ term is $\left( \frac{n}{x} \right) + y$,the sum of $r$ terms is: