The sum of $n$ terms of an $A.P.$ is given by $S_{n} = 2n^{2} + 5n$. Then,the $n^{th}$ term of the $A.P.$ $T_{n} = \dots$

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have $27$ flags to be fixed at intervals of every $2 \,m$. The flags are stored at the position of the middle-most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much total distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag? (in $m$)

For the finite $A.P.$ $12, 21, 30, \ldots, 363,$ find the $12^{th}$ term from the end.

For a given $A.P.$,$T_{7} = 12$ and $T_{12} = 72$. Then,$d = \dots \dots \dots \dots$

Which term of the $A.P.$ $13, 20, 27, 34, \ldots$ is $384$ (in $^{th}$)?

For a given finite $A.P.$,$a=2, n=8$ and $S_{8}=72$. Then,$l=........$