Q8 of 36 Page 161

In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

At start he has to run 24m to get the first potatoe then 28 m as the next potatoe is 4m away from first and so on


Hence the sequence of his running will be


24, 28, 32, …


There are 20 terms in sequence as there are 20 potatoes


Hence only to get potatoes from starting point he has to run


24 + 28 + 32 + …upto 20 terms


This is only from starting point to potatoe but he has to get the potatoe back to starting point hence the total distance will be twice that is


Total distance ran = 2 × (24 + 28 + 32…) …(a)


Let us find the sum using he formula to find sum of n terms of AP


That is


There are 20 terms hence n = 20



⇒ S20 = 10(48 + 19(4))


⇒ S20 = 10(48 + 76)


⇒ S20 = 10 × 124


⇒ S20 = 1240 m


Using (a)


⇒ Total distance ran = 2 × 1240


⇒ Total distance ran = 2480 m


Hence total distance he has to run is 2480 m


More from this chapter

All 36 →
6

We know the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21-sided polygon.

 7

A side of an equilateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid points of the sides of the first triangle. The process is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

 9

In a cricket tournament 16 school teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. If the last placed team is awarded Rs 275 in prize money and the award increases by the same amount for successive finishing places, how much amount will the first place team receive?

 10

If a1, a2, a3, ..., an are in A.P., where ai > 0 for all i, show that