In a potato race 20 potatoes are placed in a line at intervals of 4 metres 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?

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CBSE | Class 11 | Maths | NCERT Exemplar | Sequences and Series

In a potato race 20 potatoes are placed in a line at intervals of 4 metres 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:

Given at start he needs to run 24m to get the main potato then 28 m as the following potato is 4m away from first, and so on

Thus the succession of his running will be 24, 28, 32 …

There are 20 terms in succession as there are 20 potatoes

Thus just to get potatoes from beginning stage he needs to run24 + 28 + 32 + … up to 20 terms

This is just from beginning stage to potato yet he needs to return the potato once again to beginning stage thus the absolute distance will be double that is

Total distance ran $=\text{ }2\text{ }\times \text{ }\left( 24\text{ }+\text{ }28\text{ }+\text{ }32\ldots \right)\text{ }\ldots \text{ }1$

Using the formula to find sum of n terms of AP let us now find the sum

i.e. ${{S}_{n~}}=\text{ }n/2\text{ }\left( 2a\text{ }+\text{ }\left( n\text{ }\text{-}1 \right)\text{ }d \right)$

There are 20 terms therefore $n = 20$

$\Rightarrow ~{{S}_{20}}~=\text{ }\left( 20/2 \right)\text{ }\left( 2\text{ }\left( 24 \right)\text{ }+\text{ }\left( 20\text{-}\text{ }1 \right)\text{ }4 \right)$