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 is: An = A1 + (n - 1) * d, where An represents the amount of money in the account after the nth month, A1 is the initial deposit, n is the number of months, and d is the common difference.
In this case, the initial deposit, A1, is $1000, and the monthly deposit, d, is $75. So the rule is: An = 1000 + (n - 1) * 75.
b. To find out how much money is in the account after 18 months, we can substitute n = 18 into the formula and calculate the value of An.
An = 1000 + (18 - 1) * 75
= 1000 + 17 * 75
= 1000 + 1275
= $2275
Therefore, after 18 months, there will be $2275 in the account.