If the sum of $n$ terms of an $AP$ is given by $S_{n} = n^{2} + n$,then the common difference of the $AP$ is

If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0$ are in $A.P.$,then $\alpha$ is:

If $x, y, z$ are in an arithmetic progression,and $a$ is the arithmetic mean of $x$ and $y$,and $b$ is the arithmetic mean of $y$ and $z$,then what is the arithmetic mean of $a$ and $b$?

If the sides of a right-angled triangle are in $A.P.$,then their ratio is:

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

Find the mean of the first $n$ terms of the $A$.$P$. $a, (a + d), (a + 2d), \dots$