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, ……

Question.1.
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

Question.2.
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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