On Roy’s first birthday, his grandfather placed $100 in a bank account. On Roy’s second birthday, his grandfather placed $80 in the account and continued to place $80 each passing year. The arithmetic sequence 100, 180, 260, 340,… indicates the account balance for the first four years. 1 point)

Question

On Roy’s first birthday, his grandfather placed $100 in a bank account. On Roy’s second birthday, his grandfather placed $80 in the account and continued to place $80 each passing year. The arithmetic sequence 100, 180, 260, 340,… indicates the account balance for the first four years. 1 point)
Responses

f(n)=80+(n−1)100
f left parenthesis n right parenthesis equals 80 plus left parenthesis n minus 1 right parenthesis 100

f(n)=80(100)n−1
f left parenthesis n right parenthesis equals 80 left parenthesis 100 right parenthesis superscript n minus 1 baseline

f(n)=100+80(n)
f left parenthesis n right parenthesis equals 100 plus 80 left parenthesis n right parenthesis

f(n)=100+(n−1)80

GPT-4o mini · Answer

To model the account balance for Roy after $ n $ years, we can analyze the deposits made by his grandfather:

On the first birthday ($ n = 1 $), the account balance is $ 100 $.
On the second birthday ($ n = 2 $), the balance is $ 100 + 80 = 180 $.
On the third birthday ($ n = 3 $), the balance is $ 100 + 80 + 80 = 260 $.
On the fourth birthday ($ n = 4 $), the balance is $ 100 + 80 + 80 + 80 = 340 $.

We see that the initial deposit is $ 100 $, and every subsequent year, an additional $ 80 $ is added.

Thus, the general formula for the total balance after $ n $ years can be represented as follows:

\[ f(n) = 100 + 80(n - 1) \]

This is because for every year after the first, $ 80 $ is added. The term $ (n - 1) $ accounts for the additional years after the first birthday.

So, the correct option from the given responses is:

f(n) = 100 + 80(n - 1)