Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
b) Write an explicit formula to represent the sequence.
c) Find the value of the computer at the beginning of the 6th year.
a) The sequence formed by the value of the computer at the beginning of each year is geometric, because it is decreasing by a constant percentage each year.
b) The explicit formula to represent the sequence is:
\[ V_n = 1250(0.9)^{n-1} \]
where V_n represents the value of the computer at the beginning of the nth year.
c) To find the value of the computer at the beginning of the 6th year, we substitute n = 6 into the formula:
\[ V_6 = 1250(0.9)^{6-1} \]
\[ V_6 = 1250(0.9)^5 \]
\[ V_6 = 1250(0.59049) \]
\[ V_6 = 736.86 \]
Therefore, the value of the computer at the beginning of the 6th year is $736.86.