If the $7^{th}$ term of an $A.P.$ is $40$,then the sum of the first $13$ terms is:

There are $n$ arithmetic means between $7$ and $71$. If the $5^{th}$ arithmetic mean is $27$,then $n = ......$

Let the sum of the first three terms of an $A.P.$ be $39$ and the sum of its last four terms be $178.$ If the first term of this $A.P.$ is $10,$ then the median of the $A.P.$ is

Suppose that all the terms of an arithmetic progression $(A.P.)$ are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6:11$ and the seventh term lies between $130$ and $140$,then the common difference of this $A.P.$ is

The sum of the common terms of the following three arithmetic progressions:
$3, 7, 11, 15, \ldots, 399$
$2, 5, 8, 11, \ldots, 359$ and
$2, 7, 12, 17, \ldots, 197$,is equal to $................$.

If the $m^{th}$ terms of the sequences $63, 65, 67, 69, \dots$ and $3, 10, 17, 24, \dots$ are equal,then $m = \dots$