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 here turns 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.
Total numbers of trees = 25
Distance between trees = 5
Total distance between well and first tree is = 10 m
Now, gardener return back to well after watering each tree then,
Distance between well and second tree is = 10 + 10 + 5 = 25
Distance between well and third tree = 25 + 5 + 5 = 35
Distance between well and fourth tree = 35 + 5 + 5 = 45
Distance between well and last tree without return back = 10 + 24(5) = 10 + 120 = 130
So, common difference = 35 – 25 = 10
Now, Total distance covered by 24 trees,
We knew, Sn= 
[2a + (n – 1) d]
= 
[2(25) + (24 – 1) 10]
= 12 [50 + 23 * 10]
= 12 [50 + 230]
= 12 * 280
= 3360
Now, distance covered by 25 trees = 10 + 3360 = 3370
Total distance covered by gardener with return back = 3370 + 130 = 3500 m
Hence, total distance will covered by gardener is 3500.