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.
10 years ago
11 months ago
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.