Final answer:
The explicit formula for the bids in the online auction is Bn = B1 + (n-1)d, where Bn represents the nth bid, B1 represents the first bid, and d represents the common difference. The ninth bid can be calculated by plugging in n=9 into the formula.
Step-by-step explanation:
In an arithmetic sequence, each term is calculated by adding a common difference to the previous term. In this case, the bids in the online auction are represented by an arithmetic sequence, where each bid is increasing by a constant amount.
To find the explicit formula for this sequence, we need to identify the first term (B1), the common difference (d), and the position of the term we want to find (n). In this problem, B1 is not given, but we can assume that it is the first bid made in the auction. The common difference, d, can be calculated by finding the difference between any two consecutive bids in the sequence.
For example, if the first three bids are 10, 15, and 20, then the common difference is 5. This means that each subsequent bid will increase by 5. Now, we can use this information to construct the explicit formula for the bids.
The formula for an arithmetic sequence is Bn = B1 + (n-1)d, where Bn represents the nth term in the sequence. In our case, B1 is the first bid, which we do not know, and d is the common difference that we calculated earlier. This formula tells us that to find the nth term, we need to add the common difference (d) to the first term (B1) n-1 times.
To find the ninth bid, we simply need to plug in n=9 into the formula. This gives us B9 = B1 + (9-1)d, which simplifies to B9 = B1 + 8d. This means that the ninth bid is the first bid (B1) plus 8 times the common difference (d). Therefore, to find the ninth bid, we need to know the value of B1 and d.
In conclusion, the explicit formula for the bids in the online auction is Bn = B1 + (n-1)d, where Bn represents the nth bid, B1 represents the first bid, and d represents the common difference. To find the ninth bid, we need to plug in n=9 into the formula and simplify. This gives us B9 = B1 + 8d, which means that the ninth bid is the first bid plus 8 times the common difference.