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?
[NCERT EXEMPLAR]

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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,
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.
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$As, a_{2} - a_{1} = 56 - 48 = 8 and a_{3} - a_{2} = 64 - 56 = 8 i . e . a_{2} - a_{1} = a_{3} - a_{2} So, a_{1}, a_{2}, a_{3}, . . . are in A . P . Also, a = 48, d = 8, n = 20 Now, S_{20} = \frac{20}{2} [2 a + (20 - 1) d] = 10 [2 \times 48 + 19 \times 8] = 10 \times (96 + 152) = 10 \times 248 = 2480$

So, he would have to run 2480 m to bring back all the potatoes.

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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? [NCERT EXEMPLAR]

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?
[NCERT EXEMPLAR]