You start an investment account with $3000 and save $100 each month. Write a rule to represent the total amount of money you invest in the account as an arithmetic sequence. How much money will you have invested after 12 months?
A = 3000 + 100m
A(12) = 3000 + 100(12)
To represent the total amount of money you invest in the account as an arithmetic sequence, we need to find a rule that relates the position of each term to the value of that term.
In this case, the first term represents the initial investment of $3000, and each subsequent term represents an additional $100 saved per month. The position number is equal to the number of months elapsed.
Therefore, the rule can be represented as:
Term = 3000 + (n - 1) * 100
Where Term refers to the total amount of money you have invested after n months.
To find how much money you will have invested after 12 months, we substitute n = 12 into the equation:
Term = 3000 + (12 - 1) * 100
= 3000 + 11 * 100
= 3000 + 1100
= 4100
So, after 12 months, you will have invested $4100.