Question

enzos profit has been falling. in december he made $900, in january he made $500, and in march he lost $300. select all parts of the recursive formula for the sequence.
a. $a_1 = 900$
b. $a_1 = 400$
c. $a_n = a_{n - 1} + 400$
d. $a_n = a_{n - 1} - 400$
e. $a_n = a_{n - 1} - 200$

Explanation:

Step1: Identify initial term

The first given value is December's profit, which is $\$900$, so $a_1 = 900$.

Step2: Calculate common difference

Find the change from December to January: $500 - 900 = -400$. Verify with the gap (January to March is 2 months, so $-300 - 500 = -800$, divided by 2 intervals gives $-400$ per month). The recursive formula for an arithmetic sequence is $a_n = a_{n-1} + d$, so $a_n = a_{n-1} - 400$.

Answer:

A. $a_1 = 900$
D. $a_n = a_{n-1} - 400$