Question

Roberta is selling a purse online. The online bidding increases $5 for each bid after the initial $60 bid. The table below represents the situation.

Bid number 1
2
3
4
Bid amount

Which function represents the arithmetic sequence?
A.f(n)=5n+5

B.f(n)=5n−55

C.f(n)=−5n+55

D.f(n)=5n+55

Answer 1

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 \( n \):

1. The initial bid when \( n=1 \) is $60.
2. The second bid (when \( n=2 \)) would then be \( 60 + 5 = 65 \).
3. The third bid (when \( n=3 \)) would be \( 65 + 5 = 70 \).
4. 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. \( f(n) = 5n + 55 \)**.