ln a potato race 20 potatoes arc placed in a line at intervals of 4 m with the first potato 24 m from the starting point. A contestant is required to being the potatoes back to the starting place on at a time. How far would he run in bringing back all the potatoes?

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2485 m

2480 m

2482 m

None of these

answer is B.

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Detailed Solution

According to the given condition, the sequence becomes, 24,28,...,20th term,

Here,

$\begin{array}{l} a = 24, d = 28 - 24 = 4, n = 20 \\ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ = \frac{20}{2} [2 \times 24 + (20 - 1) 4] \\ = 10 (48 + 76) \\ = 10 \times 124 \\ = 1240 \end{array}$

The contestant is required to bring the potatoes back to the starting place $= 2 S_{n} = 2 \times 1240 = 2480 m$

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