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.
a. this is a arithmetic series, not a sequence. the Sum of the series is given by months m is
sum=m/2 * (2*1000 + (m-1)75)
for 18 months, put m=18 and compute.
a. To represent the amount of money in the account as an arithmetic sequence, we can use the formula: an = a1 + (n - 1)d
Where:
an = the amount of money in the account after n months
a1 = the initial deposit ($1000)
d = the common difference ($75)
So, the rule that represents 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 formula and simplify:
a18 = 1000 + (18 - 1)75
a18 = 1000 + 17 * 75
a18 = 1000 + 1275
a18 = 2275
Therefore, there will be $2275 in the account after 18 months.