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

Let $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$,and let $w_1, w_2, \ldots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$,where $d_1 d_2 = 10$. For each $i = 1, 2, \ldots, 100$,let $R_i$ be a rectangle with length $l_i$,width $w_i$,and area $A_i$. If $A_{51} - A_{50} = 1000$,then the value of $A_{100} - A_{90}$ is:

If the $n^{th}$ terms of two $A.P.$'s are $3n + 8$ and $7n + 15$,then the ratio of their $12^{th}$ terms will be:

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and the product of the remaining two middle terms is $15$,then the greatest number of the series will be:

If $a, b, c$ are in $A.P.$,then $\frac{1}{\sqrt{a} + \sqrt{b}}, \frac{1}{\sqrt{a} + \sqrt{c}}, \frac{1}{\sqrt{b} + \sqrt{c}}$ are in

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in an arithmetic progression,then $2p^3-3pq=$