To determine if the sequence formed by the value of the computer each year is arithmetic, geometric, or neither, we need to consider how the value is changing each year.
Since the computer depreciates by 10% each year, it is decreasing in value by a constant percentage. This means that the sequence formed by the value at the beginning of each year is a geometric sequence.
The explicit formula for a geometric sequence is given by the formula:
\[a_n = a_1 * r^{(n-1)}\]
where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
In this case, \(a_1 = 1250\) (the initial value of the computer) and \(r = 1 - 0.10 = 0.90\) (the value decreases by 10% each year).
So, the explicit formula for the sequence would be:
\[a_n = 1250 * 0.90^{(n-1)}\]
To find the value of the computer at the beginning of the 6th year, we substitute \(n = 6\) into the formula:
\[a_6 = 1250 * 0.90^{(6-1)}\]
\[a_6 = 1250 * 0.90^5\]
\[a_6 = 1250 * 0.59049\]
\[a_6 = 738.1125\]
Therefore, the value of the computer at the beginning of the 6th year is $738.11.
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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.
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.
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