Question

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. Which recursive formula models the total amount of money still owed, mc022-1.jpg?

Answer 1

The recursive formula that models the amount owed is
an = a(n-1) -75; a1 = 600. 
This formula is for AFTER the first month of payment, this is why the first term is 700-100 = 600. This also means that n > 1.

Answer 2

Answer:

Option B is correct

$a_n = a_{n-1}-75$ ; $a_1 = 600$

Step-by-step explanation:

The recursive formula for the arithmetic sequence is given by:

$a_n = a_{n-1}+d$              .....[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, $a_1 = 600$

and d = -75

Since,

525-600 = -75

450-525 = -75 and so on...

Substitute the given values in [1] we have;

$a_n = a_{n-1}-75$

Therefore, the recursive formula models the total amount of money still owed is:

$a_n = a_{n-1}-75$ ; $a_1 = 600$