If $a_1, a_2, a_3, \dots$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$,then the sum of the first $15$ terms of this $A.P.$ is

If the $n^{th}$ term of an arithmetic progression is $\frac{(2n + 1)}{3}$,what is the sum of its first $19$ terms?

If the sum of the first $21$ terms of the series $\log _{9^{1 / 2}} x + \log _{9^{1 / 3}} x + \log _{9^{1 / 4}} x + \dots$ where $x > 0$ is $504$,then $x$ is equal to:

The first term of an arithmetic progression is $10$ and the last term is $50$. If the sum of all its terms is $300$,then the number of terms $n = ...$

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 $x^3+ax^2+bx+c=0$ are in arithmetic progression,then