If for an Arithmetic Progression $(AP)$,$9$ times the $9^{th}$ term is equal to $13$ times the $13^{th}$ term,then the value of the $22^{nd}$ term is:

Let $a_n, n \geq 1$,be an arithmetic progression with first term $2$ and common difference $4$. Let $M_n$ be the average of the first $n$ terms. Then the sum $\sum_{n=1}^{10} M_n$ is

Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}$, where $a > 2$. If $\alpha$ is such that $a, 4, \alpha, b$ are in $A$.$P$.,then the equation $\alpha x^2 - ax + 2(\alpha - 2b) = 0$ has :

The interior angles of a polygon are in $A.P.$ If the smallest angle is $120^o$ and the common difference is $5^o$,then the number of sides is

If the $n^{th}$ term of an $A.P.$ is $(2n - 1)$,then the sum of its first $n$ terms is

Let $S_n$ denote the sum of the first $n$ terms of an $A.P$. If $S_4 = 16$ and $S_6 = -48$,then $S_{10}$ is equal to