If all interior angles of a quadrilateral are in an $A.P.$ and the common difference is $10^{\circ}$,find the smallest angle. (in $^{\circ}$)

If the ${5^{th}}$ term of a $H.P.$ is $\frac{1}{45}$ and the ${11^{th}}$ term is $\frac{1}{69}$,then its ${16^{th}}$ term will be:

If $a, b, c, d$ and $p$ are different real numbers such that $(a^2 + b^2 + c^2)p^2 - 2(ab + bc + cd)p + (b^2 + c^2 + d^2) \le 0$,then $a, b, c, d$ are in

If $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n}$ is the $A.M.$ of $a$ and $b$,then $n = $

Let $S_1, S_2, \dots, S_{101}$ be the consecutive terms of an $A.P.$ If $\frac{1}{S_1 S_2} + \frac{1}{S_2 S_3} + \dots + \frac{1}{S_{100} S_{101}} = \frac{1}{6}$ and $S_1 + S_{101} = 50$, then $|S_1 - S_{101}|$ is equal to

If the first term of a $G.P.$ is $5$ and the common ratio is $-5$,then which term is $3125$ (in $^{th}$)?