A friend opens a savings account by depositing $1000. He deposits an additional $75 into the account each month.
a. What is a rule that represents the amount of money in the account as an arithmetic sequence?
b. How much money is in the account after 18 months? Show your work.
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a. The rule that represents the amount of money in the account as an arithmetic sequence can be given by the formula:
An = A1 + (n-1)d
Where:
An = The nth term of the sequence (amount of money in the account after n months)
A1 = The initial deposit into the account
n = The number of months
d = The common difference (the additional amount deposited each month)
In this case, the initial deposit is $1000, so A1 = 1000, and the additional amount deposited each month is $75, so d = 75.
Therefore, the rule representing the amount of money in the account as an arithmetic sequence is:
An = 1000 + (n-1)75
b. To find the amount of money in the account after 18 months, we can substitute n = 18 into the rule we derived in part a.
An = 1000 + (18-1)75
Simplifying,
An = 1000 + 17*75
= 1000 + 1275
= 2275
Therefore, there will be $2275 in the account after 18 months.