There are 25 trees at equal distances of 5 meters in a line with a well, the distance of well from the nearest tree being 10 meters. 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.
Given: total trees are 25 and equal distance between two adjacent trees are 5 meters
To find: the total distance the gardener will cover
As gardener is coming back to well after watering every tree
Distance covered by him to water 1st tree and return to the initial position is 10m + 10m = 20m
Now, distance between adjacent trees is 5m
Distance covered by him to water 2nd tree and return to the initial position is 15m + 15m = 30m
Distance covered by the gardener to water 3rd tree return to the initial postion is 20m + 20m = 40m
Hence distance covered by the gardener to water the trees are in A.P
A.P. is 20, 30, 40 ………upto 25 terms
Here first term,a = 20,common difference, d = 30 – 20 = 10
And n = 25
We need to find S25 which will be the total distance covered by gardener to water 25 trees
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
⇒ S25 = 25(140)
⇒ S25 = 3500
Hence, total distance covered by gardener to water trees is 3500 m