We have a question from arithmetic progression chapter in which we have given that 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.
Book RS Aggarwal, Class 10, Chapter 5C, question no 43.
The distance of nearest tree is 10m
so that distance travelled to water nearest tree =20m ……. (10×2=20m)
The distance of next nearest tree is 10+5=15m
so total distance travelled =15×2=30m
following form an A.P of terms : – (20,30,40,50.........)
∴ We have to find total distance travelled,
∴ we have to find S25
n=25,a=20d=10
∴Sn=n/2(2a+(n−1)d)→ formula
∴S25=25/2(2×20+(25−1)10)
∴S25=25/2(40+24×10)
∴S25=25(20+120)
∴S25=25×140
∴S25=3500m
Total distance traveled is 3500m