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.
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.
Let $S_{n}$ be the total distance travelled by the gardener.
Let d be the common difference (distance) between two trees. Let a be the distance of the well from the first tree.
Here, n = 25, d = 10, a = 20
Distance travelled by the gardener from the well to the last tree $=S_{25}$
$S_{25}=\frac{25}{2}\{2 \times 20+(25-1) 10\}$
$=\frac{25}{2}(40+240)$
$=3500 \mathrm{~m}$
Therefore, the total distance the gardener has to travel is 3500 m.