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 $9^{th}$ and $19^{th}$ terms of an arithmetic progression are $35$ and $75$ respectively,what is its $20^{th}$ term?

If for an arithmetic progression $S_{2n} = 2S_n$,then $S_{3n} / S_n = \dots$

$A$ person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{th}$ minute. If $a_1 = a_2 = \ldots = a_{10} = 150$ and $a_{10}, a_{11}, \ldots$ are in an $A.P.$ with common difference $-2$,then the time taken by him to count all notes is ............... $minutes$.

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

The sum of $n$ arithmetic means between $a$ and $b$ is: