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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 . 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, .........
(i) How many bottles did they collect on June 25th?
(ii) 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.

Sagot :

Using an arithmetic sequence, it is found that:

i) They collected 300 bottles on June 25th.

ii) The day was July 18th.

What is an arithmetic sequence?

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the sequence is: {417 ,404 ,391, .........}, hence the first term is [tex]a_1 = 417[/tex], the common difference is d = -13, and the equation is:

[tex]a_n = 417 - 13(n - 1)[/tex]

Item i)

They started on June 15th, hence June 25th is the 10th day, thus:

[tex]a_{10} = 417 - 13(9) = 300[/tex]

They collected 300 bottles on June 25th.

Item ii)

This is n days after June 15th, for which [tex]a_n = 1[/tex], hence:

[tex]a_n = 417 - 13(n - 1)[/tex]

[tex]1 = 430 - 13n[/tex]

[tex]13n = 429[/tex]

[tex]n = 33[/tex]

33 days after June 15th is July 18th.

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

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