#### 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 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?

Let she fixes 13 flags on one side and 13 on other side of the middle flag.

distance covered for fixing first flag and return is 2m + 2m = 4m

distance covered for fixing second flag and return is 4m + 4m = 8m

distance covered for fixing third flag and return is 6m + 6m = 12m

Similarly for thirteen flags is

4m + 8m + 12m + …….

Here, a = 4

d = 8 - 4 = 4

n = 13

$\\ \mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}] \\ \mathrm{S}_{13}=\frac{13}{2}[2(4)+(13-1) 4] \\ \frac{13}{2}[56]=364$

Total distance covered = 364 × 2 = 728 m         (for both side )

distance, only to carry the flag = 364.