A friend opens a savings account by depositing $1000. He deposits an additional $75 into the account each month. a. What is an explicit formula 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.
A friend opens a savings account by depositing $1000. He deposits an additional $75 into the account each month. a. What is an explicit formula 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.
A friend opens a savings account by depositing $1000. He deposits an additional $75 into the account each month.
a. What is an explicit formula 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.
Expert Solution & Answer
To determine
To find: Amount of money in the account after 18 months.
Answer to Problem 6STP
Amount of money in the bank after 18 months = $2275
Explanation of Solution
Given Data:
A person opens a savings account by depositing $1000. He deposits additional $75 per month in the account.
Calculation:
The series is in Arithmatic ProgressionThus, the sequence is given by:an=a+(n−1)dNow,a=1000d=75n=18Thus,a18=1000+(18−1)75a18=1000+1350−75a18=2350−75a18=2275Therefore,Amount of money in the bank after 18 months = $2275
Conclusion:
Amount of money in the bank after 18 months = $2275
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