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

Distance covered by the gardener to water the first tree and return to the water tank = 10 m + 10 m = 20 m

Distance covered by the gardener to water the second tree and return to the water tank = 15 m + 15 m = 30 m

Distance covered by the gardener to water the third tree and return to the water tank = 20 m + 20 m = 40 m and so on.

∴ Total distance covered by the gardener to water all the trees = 20 m + 30 m + 40 m + ... up to 25 terms

This series is an arithmetic series.

Here, a = 20, d = 30 − 20 = 10 and n = 25

Using the formula, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$, we get

$S_{25}=\frac{25}{2}[2 \times 20+(25-1) \times 10]$

$=\frac{25}{2}(40+240)$

$=\frac{25}{2} \times 280$

$=3500$

Hence, the total distance covered by the gardener to water all the trees 3500 m.