# There are 25 trees at equal distances of 5 metres in a line with a well,

Question:

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 water 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 eater all the trees.

Solution:

In the given problem, there are 25 trees in a line with a well such that the distance between two trees is 5 meters and the distance between the well and the first tree is 10 meters.

So, the total distance covered to water first tree

Then he goes back to the well to get water.

So,

The total distance covered to water second tree

The total distance covered to water third tree

The total distance covered to water fourth tree

So, from second tree onwards, the distance covered by the gardener forms an A.P. with the first term as 25 and common difference as 10.

So, the total distance covered for 24 trees can be calculated by using the formula for the sum of n terms of an A.P,

$S_{\pi}=\frac{n}{2}[2 a+(n-1) d]$

We get,

$S_{n}=\frac{24}{2}[2(25)+(24-1)(10)]$

$=12[50+(23)(10)]$

$=12(50+230)$

$=12(280)$

$=3360$

So, while watering the 24 trees he covered 3360 meters. Also, to water the first tree he covers 10 meters. So the distance covered while watering 25 trees is 3370 meters.

Now, the distance between the last tree and the well

$=10+120$

$=130$

So, to get back to the well he covers an additional 130 m. Therefore, the total distance covered by the gardener

Therefore, the total distance covered by the gardener is.