Question

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 he returns to the well after watering each tree to get water for the next. Find the total distance(in meters) the gardner will cover in order to water all the trees.

Answer 1

The distance of nearest tree is $10m$

so that distance travelled to water nearest tree $=20m$ ....... $(10\times 2=20m)$

The distance of next nearest tree is $10+5=15m$

so total distance travelled $=15\times 2=30m$

following form an A.P of terms : - $(20,30,40,\mathrm{50.........})$

$\therefore$ We have to find total distance travelled,

$\therefore$ we have to find $S_{25}$

$n=25,a=20d=10$

$\therefore S_n=\frac{n}{2}(2a+(n-1\left)d\right)\to$ formula

$\therefore S_{25}=\frac{25}{2}(2\times 20+(25-1\left)10\right)$

$\therefore S_{25}=\frac{25}{2}(40+24\times 10)$

$\therefore S_{25}=25(20+120)$

$\therefore S_{25}=25\times 140$

$\therefore S_{25}=3500m$

Total distance traveled is $3500m$