$2+3+5+6+8+9+\ldots$ to $2n$ terms $=$

The sum of three terms of an Arithmetic Progression $(AP)$ is $18$ and the sum of their squares is $158$. The largest term is.......

If the ratio of the sum of $n$ terms of two arithmetic progressions is $2n + 3 : 6n + 5$,then the ratio of their $13^{th}$ terms is.......

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an arithmetic progression are $1/a$,$1/b$,and $1/c$ respectively,then $ab(p - q) + bc(q - r) + ca(r - p) = \dots$

If $a, b, c$ are in Arithmetic Progression,then $\frac{1}{\sqrt{b} + \sqrt{c}}, \frac{1}{\sqrt{c} + \sqrt{a}}, \frac{1}{\sqrt{a} + \sqrt{b}}$ are in:

If the sum of the first $2n$ terms of the arithmetic progression $2, 5, 8, \dots$ is equal to the sum of the first $n$ terms of the arithmetic progression $57, 59, 61, \dots$,then $n = \dots$