Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
1. Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither?
2. Explain. Write an explicit formula to represent the sequence.
3. Find the value of the computer at the beginning of the 6th year.
1. The sequence formed by the value of the computer at the beginning of each year is geometric.
2. The explicit formula to represent the sequence is:
a_n = 1250(0.9)^n-1
where a_n is the value of the computer at the beginning of the nth year, n represents the year number starting from 1, and 0.9 is the factor representing the 10% depreciation.
3. To find the value of the computer at the beginning of the 6th year, we plug in n = 6 into the formula:
a_6 = 1250(0.9)^6-1
a_6 = 1250(0.9)^5
a_6 = 1250(0.59049)
a_6 = 737.94
Therefore, the value of the computer at the beginning of the 6th year is $737.94.