Case Study Question 07


Chapter 5: Arithmetic Progressions

Class 10

Accumulation of plastics in the environment creates problems for wildlife and their habitats as well as for human. Plastics are a threat to the environment. The children of Avantipur decided that they would contribute their service to put an end to the usage of plastics in their village. They fixed posters and hoisted placards which depicted the ill effects of plastics on human health and environment. They started their work on June `15^{th}`. They started collecting the thrown off plastic bottles in their locality and started counting them.
To their astonishment, they found that the number of plastic bottles that they collected each day were in Arithmetic Progression which went like this: 417, 404, 391, ……

How many bottles did they collect on June `25^{th}`?

417, 404, 391, ……
As the children started collecting plastics on June `15^{th}`, June `25^{th}` falls on the `11^{th}` day `\Rightarrow n = 11`
`\Rightarrow a_{n} = a + (11-1) d = 287` bottles

The children of Avantipur wanted to make their village a plastic free zone. Identify the day on which they got 1 bottle which was their dream day.

The AP is 417, 404, 391, ……
`a=417`, `d=(-13)`
Let the day on which they got 1 bottle be the `n^{th}` day
`\Rightarrow a_{n}=1`
`\Rightarrow  a +(n-1)d =1`
`\Rightarrow 417 +(n-1)(-13) =1`
`\Rightarrow n = 33`
Their dream day was on the `33^{rd}` day starting from June `15^{th}`. Hence the day falls on July `17^{th}`.

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