1. Tardigrade
  2. Question
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  4. There are 25 trees at equal distances of 5 meters 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 he returns to the well after watering each tree to get water for the next. The total distance the gardener will cover in order to water all the trees is

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Q. There are $25$ trees at equal distances of $5$ meters 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 he returns to the well after watering each tree to get water for the next. The total distance the gardener will cover in order to water all the trees is

Sequences and Series

Solution:

Obviously the well (W) must be on one side of the trees $T _{1}, T _{2}, ......., T_{25}$,
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The total distance covered by the gardener
$= WT _{1}+\left(2 WT _{1}+ T _{1} T _{2}\right)+\left(2 WT _{2}+ T _{2} T _{3}\right)+.....+\left(2 WT _{24}+ T _{24} T _{25}\right]$
$=10+(2 \times 10+5)+(2 \times 15+5) +............+$ to 25 terms
$=10+(25+35+45+.......... $ to 24 terms )
$=10+\frac{24}{2}[2 \times 25+(24-1) \times 10]$
$=10+12[50+230]=3370$