# In a potato race,

To pick the first potato, the competitor has to run 5 m to reach the potato and 5 m to run back to the bucket.

Total distance covered by the competitor to pick first potato = 2 × (5) = 10 m

To pick the second potato, the competitor has to run (5 + 3) m to reach the potato and (5 + 3) m to run back to the bucket.

Total distance covered by the competitor to pick second potato = 2 × (5 + 3) = 16 m

To pick the third potato, the competitor has to run (5 + 3 + 3) m to reach the potato and (5 + 3 + 3) m to run back to the bucket.

Total distance covered by the competitor to pick third potato = 2 × (5 + 3 + 3) = 22 m

This will continue and we will get a sequence of distance as 10, 16, 22,… upto 10 terms (as there are 10 potatoes to pick).

Total distance covered by the competitor to pick all the 10 potatoes = 10 + 16 + 22 + … upto 10 terms.

This forms an Arithmetic series with first term = a = 10

and Common difference = d = 6

Number of terms = n = 10

Now, S10 = (10/2)[2a + (10 - 1)d]

= 5 × [2(10) + 9(6)]

= 5 × [20 + 54]

= 5 × 74

= 370

Total distance covered by the competitor = 370 m

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