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

The sum of $3+5+7+\ldots$ to $n$ terms is:

Let $a_1, a_2, a_3, \ldots, a_{11}$ be real numbers satisfying $a_1=15$,$27-2a_2 > 0$,and $a_k = 2a_{k-1} - a_{k-2}$ for $k = 3, 4, \ldots, 11$. If $\frac{a_1^2 + a_2^2 + \ldots + a_{11}^2}{11} = 90$,then the value of $\frac{a_1 + a_2 + \ldots + a_{11}}{11}$ is equal to

If $A$ is an arithmetic mean between two numbers and $S$ is the sum of $n$ arithmetic means between the same two numbers,then:

If the sum of the first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms,then find the sum of the first $(p+q)$ terms.

The number of terms of an $A.P.$ is even; the sum of all the odd terms is $24$,the sum of all the even terms is $30$ and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the $A.P.$ is: