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.

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