There are 25 trees at equal distances of 5 m in a line with a water tank, the distance of the water tank from the nearest tree being 10 m. A gardener waters all the trees separately, starting from the water tank and returning back to the water tank after watering each tree to get water for the next. Find the total distance covered by the gardener in order to water all the trees.
To water the first tree, the gardener has to cover 10 m to reach the tree and 10 m to go back to the tank.
∴ Total distance covered by the gardener to water first tree = 2 × (10) = 20 m
To water the second tree, the gardener has to cover (10 + 5) m to reach the tree and (10 + 5) m to go back to the tank.
∴ Total distance covered by the gardener to water second tree = 2 × (10 + 5) = 30 m
To water the third tree, the gardener has to cover (10 + 5 + 5) m to reach the tree and (10 + 5 + 5) m to go back to the tank.
∴ Total distance covered by the gardener to water third tree = 2 × (10 + 5 + 5) = 40 m
This will continue and we will get a sequence of distance as 20, 30, 40,… upto 25 terms (as there are 25 trees to be watered).
Total distance covered by the gardener to water all 25 trees = 20 + 30 + 40 + … upto 25 terms.
This forms an Arithmetic series with first term = a = 20
and Common difference = d = 10
Number of terms = n = 25
Now, S25 = (25/2)[2a + (25 - 1)d]
= (25/2) × [2(20) + 24(10)]
= (25/2) × [40 + 240]
= (25/2) × 280
= 25 × 140
= 3500
∴ Total distance covered by the gardener = 3500 m