invest $ 3000 and save $100 each month. Write a rule to represent the total amount of money invest into your account as arithmetic sequence. How much money will you have invested after 12 month?
INVEST(t)=3000+100*t
To represent the total amount of money invested into your account as an arithmetic sequence, we can use the formula for arithmetic sequences:
An = A1 + (n - 1)d
Where:
An is the nth term of the sequence (the total amount invested after n months),
A1 is the initial term of the sequence (the initial investment),
n is the number of terms (number of months),
d is the common difference (monthly savings).
In this case:
A1 = $3000 (initial investment)
n = 12 (number of months)
d = $100 (monthly savings)
Plugging these values into the formula, we can calculate the total amount invested after 12 months:
A12 = $3000 + (12 - 1) * $100
A12 = $3000 + 11 * $100
A12 = $3000 + $1100
A12 = $4100
Therefore, you will have $4100 invested after 12 months.