Answer:
recursive formula represents the total amount of money in the bank is given by \(a_{n+1}=a_n(1.02)^n+15\)
Step-by-step explanation:
Given : Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance.
We have to write a recursive formula representing the total amount of money in the bank.
Since, she has $200 in her account so first term is 200
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and At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance.
balance at beginning of year 1 = 200+15=215
\(a_1=215\)
at the beginning of year 1 she has balance = 215 + interest on 215 + 15
\((1+\frac{r}{100})^n\) , where n is time period.
r = 2%
\((1+\frac{2}{100})^n=(1.02)^n\)
Thus, at the beginning of year 1 she has balance =\(a_2=215(1.02)+15\)
So at every next year she will have interest on previous balance + $15
So , recursive formula represents the total amount of money in the bank is given by \(a_{n+1}=a_n(1.02)^n+15\)