Question

# 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? Polynomial arithmetic ANSWERED 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?

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.