The natural numbers are arranged in rows as follows:
$1$
$2, 3$
$4, 5, 6$
$7, 8, 9, 10$
$. . .$
What is the sum of the numbers in the $n^{th}$ row?

In an $A.P.$,the first term is $2$ and the sum of the first five terms is one-fourth of the next five terms. Show that the $20^{th}$ term is $-112$.

Let $A, G, H$ and $S$ respectively denote the arithmetic mean,geometric mean,harmonic mean and the sum of the numbers $a_1, a_2, a_3, \ldots, a_n$. Then the value of $x$ at which the function $f(x)=\sum_{k=1}^n(x-a_k)^2$ has a minimum is

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic sequence are $a$,$b$,and $c$ respectively,then the value of $[a(q - r) + b(r - p) + c(p - q)]$ is:

Suppose $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ is an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of the first nine terms of the progression is $5:17$ and $110 < a_{15} < 120$,then the sum of the first ten terms of the progression is equal to -

What is the sum of all integers between $81$ and $719$ that are divisible by $5$?