If $a, b, c, d, e, f$ are in an arithmetic progression,then $e - c = \dots$

If the sum of $n$ terms of an $A.P.$ is $nA + n^2B$,where $A$ and $B$ are constants,then its common difference will be

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

There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is

If $\log _{3} 2, \log _{3}(2^{x}-5), \log _{3}(2^{x}-\frac{7}{2})$ are in an arithmetic progression,then the value of $x$ is equal to $.....$

Consider an $A.P.$ of positive integers,whose sum of the first three terms is $54$ and the sum of the first twenty terms lies between $1600$ and $1800$. Then its $11^{\text{th}}$ term is: