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. 5.6).

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. 5.6).

Solution:

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.
The distances of potatoes are as follows. 5, 8, 11, 14, ...
This squence is an A.P.
So, First term, a = 5
Common difference, d = 8 - 5 = 3
Number of terms, n = 10
We know that the sum of n terms Sₙ = n/2 [2a + (n - 1) d]
S₁₀= 10/2 [2 × 5 + (10 - 1) × 3]
= 5 (10 + 27) = 5 × 37
= 185
Every time player has to run back to the bucket,
therefore, the total distance that the competitor has to run will be two times the total distance.
Hence, The total distance that the competitor will run = 2 × 185 m = 370 m