To determine the function that represents the arithmetic sequence for the bidding on the purse, we need to consider the information provided:
- The initial bid (bid number 1) is $60.
- Each subsequent bid increases by $5.
We can represent the bid amount as a function of the bid number \( n \):
- The initial bid when \( n=1 \) is $60.
- The second bid (when \( n=2 \)) would then be \( 60 + 5 = 65 \).
- The third bid (when \( n=3 \)) would be \( 65 + 5 = 70 \).
- The fourth bid (when \( n=4 \)) would be \( 70 + 5 = 75 \).
This pattern shows that with each increase in bid number, the amount increases by $5.
Now we can express the bid amount mathematically. The first bid can be represented as:
- For \( n = 1 \): \( f(1) = 60 \)
- For \( n = 2 \): \( f(2) = 60 + 5(1) = 65 \)
- For \( n = 3 \): \( f(3) = 60 + 5(2) = 70 \)
- For \( n = 4 \): \( f(4) = 60 + 5(3) = 75 \)
The general term for an arithmetic sequence can be expressed as:
\[ f(n) = a + (n - 1) d \]
where:
- \( a \) is the first term (60),
- \( d \) is the common difference (5),
- \( n \) is the bid number.
So:
\[ f(n) = 60 + (n - 1) 5 = 60 + 5n - 5 = 5n + 55 \]
Thus, the function that represents the arithmetic sequence is:
D. \( f(n) = 5n + 55 \).
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