There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next.

To do:

We have to find the total distance the gardener will cover in order to water all the trees. Solution:

Total number of trees $=25$

Distance between each tree $= 5\ m$

Distance between first tree and the well $= 10\ m$

The distance covered by the gardener to water the first tree $=10\ m + 10\ m = 20\ m$

The distance covered by the gardener to water the second tree $=15\ m + 15\ m = 30\ m$

The distance covered by the gardener to water the third tree $=20\ m + 20\ m = 40\ m$ The distances covered by the gardener to water each successive tree (in m) is, $20, 30, 40, .....$

This series is in A.P. where $a = 20, d = 30 – 20 = 10$ and $n = 25$

We know that,

\( \mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d] \) Total distance covered by the gardener \( \mathrm{S}_{25}=\frac{n}{2}[2 a+(n-1) d] \) \( =\frac{25}{2}[2 \times 20+(25-1) \times 10] \) \( =\frac{25}{2}[40+24 \times 10] \)