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 geometric, as the value decreases by a constant percentage each year.
The formula to represent the sequence is:
V(n) = $1,250 * (0.9)^n
where V(n) is the value of the computer at the beginning of the nth year.
To find the value of the computer at the beginning of the 6th year, we substitute n = 6 into the formula:
V(6) = $1,250 * (0.9)^6
V(6) = $1,250 * 0.531441
V(6) = $664.30
Therefore, the value of the computer at the beginning of the 6th year will be $664.30.