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Question
In a potato race 20 potatoes are placed in a line at intervals of 4 meters 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?
Solution
We have,
the distance travelled to bring the first potato, a1 = 2 \[\times\]24 = 48 m,
the distance travelled to bring the second potato, a2 = 2 \[\times\] (24 + 4) = 56 m,
the distance travelled to bring the third potato, a3 = 2 \[\times\] (24 + 4 + 4) = 64 m,
\[\text { As, } a_2 - a_1 = 56 - 48 = 8\text { and } a_3 - a_2 = 64 - 56 = 8\]
\[\text { i . e } . a_2 - a_1 = a_3 - a_2 \]
\[\text { So, } a_1 , a_2 , a_3 , . . . \text { are in A . P } . \]
\[\text { Also, } a = 48, d = 8, n = 20\]
\[\text { Now }, \]
\[ S_{20} = \frac{20}{2}\left[ 2a + \left( 20 - 1 \right)d \right]\]
\[ = 10\left[ 2 \times 48 + 19 \times 8 \right]\]
\[ = 10 \times \left( 96 + 152 \right)\]
\[ = 10 \times 248\]
\[ = 2480\]
So, he would have to run 2480 m to bring back all the potatoes.
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