Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
Write an explicit formula to represent the sequence.
Find the value of the computer at the beginning of the 6th year.
The sequence formed by the value of the computer at the beginning of each year is a geometric sequence. This is because the value decreases by the same percentage (10%) each year.
The explicit formula to represent the sequence is:
V_n = $1250 * (0.9)^n
where V_n is the value of the computer at the beginning of year n.
To find the value of the computer at the beginning of the 6th year, we plug in n=6 into the formula:
V_6 = $1250 * (0.9)^6
V_6 = $1250 * 0.531441
V_6 = $664.30
Therefore, the value of the computer at the beginning of the 6th year is $664.30.