In a potato race, a bucket is placed at the starting point,
Question.

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see fig.). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? Solution:

Distance run to pick up the Ist potato

= 2 × 5 = 10 m

Distance run to pick up the IInd potato

= 2 × (5 + 3) m = 16 m

Distance run to pick up the IIIrd potato

= 2 × {5 + 3 + 3} m = 22 m

Thus, the sequence become 10, 16, 22, … to 10 terms. It forms an A.P.

Here, a = 10, d = 6 and n = 10

$S u m=S_{10}=\frac{10}{2}\{2 a+9 d\}=5 \times\{2 \times 10+9 \times 6)$

= 5 × 74 m = 370 m

Hence, the total distance run by a competitor

= 370 m.