Which of the following sequences is an $A.P.$?

An $AP$ consists of $37$ terms. The sum of the three middle most terms is $225$ and the sum of the last three is $429$. Find the $AP$.

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = \sqrt{2}, d = \frac{1}{\sqrt{2}}$

For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

Find the $45^{th}$ term of the $A.P.$ $13, 8, 3, -2, \ldots$

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 $m$)