Answer :

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, S_{25} = (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

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