Answer:
Option B is correct
[tex]a_n = a_{n-1}-75[/tex] ; [tex]a_1 = 600[/tex]
Step-by-step explanation:
The recursive formula for the arithmetic sequence is given by:
[tex]a_n = a_{n-1}+d[/tex] .....[1]
where,
d is the common difference.
n is the number of terms.
As per the statement:
Paige borrows $700 from her parents for a new computer.
She repays $100 the first month, then begins to repay her parents $75 per month.
Now, she only has to pay back after then, $700 - $100 = $600
then, begins to repay her parents $75 per month.
The sequence we get;
600, 525, 450, ....
This is the arithmetic sequence.
here, [tex]a_1 = 600[/tex]
and d = -75
Since,
525-600 = -75
450-525 = -75 and so on...
Substitute the given values in [1] we have;
[tex]a_n = a_{n-1}-75[/tex]
Therefore, the recursive formula models the total amount of money still owed is:
[tex]a_n = a_{n-1}-75[/tex] ; [tex]a_1 = 600[/tex]
