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.

\(d_2 = $ 500 - $ 800 = - $ 300.\) 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.