Enzo's profit over the last few months has been failing. In December, he made $900. In January, his profit was $500, and in March, he lost $300. is the sequence that represents his profit arithmetic? if it is, what is the recursive formula for the sequence?

Question
Polynomial arithmetic
asked 2020-11-09
Enzo's profit over the last few months has been failing. In December, he made $900. In January, his profit was $500, and in March, he lost $300. is the sequence that represents his profit arithmetic? if it is, what is the recursive formula for the sequence?

Answers (1)

2020-11-10
Step 1 Given that: Enzo's profit over the last few months has been failing. In December, he made $ 900. In January , his profit = $ 500. In March , he lost = $300. Step 2 To use : Recursive formula for arithmetic sequences , \(c(n) = c (n - 1) + d\) Where d = difference between the term . Step 3 To use the above information, To get, \(a_1 = $900 , a_2= $500, a_3 = - $300\) To get a sequence $ 900 , $ 500 , - $300. To check this sequence is arithmetic . Here, \(a(1) = $ 900 , a(2) = $ 500 , a(3) = - $300\) To find the common difference \(d_1 = $ 900 - $400 = $ 500,\)
\(d_2 = $ 500 - $ 800 = - $ 300.\) To get, \(d_1 = -$ 400 , d_2 = - $ 800.\) There is no common difference . Therefore , The given sequence is not arithmetic. Thus, The given sequence that represents his profit is not arithmetic. Step 4 Since, There is no common difference in the sequence and do not get the recursive formula for the sequence.
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