Final answer:
Upon analyzing the sequence and testing both formulas provided by Mary and Alice, neither of their proposed explicit formulas correctly match the given sequence. Thus, the correct answer is that neither Mary's formula g(n) = 14 - 9(n-1) nor Alice's formula g(n) = 14 - 9n is right.
Step-by-step explanation:
The sequence provided is 14, 10, 5, -4, -13, and you need to find an explicit formula for this sequence. To find an explicit formula, let's look at the differences between consecutive terms:
- Between 14 and 10, the difference is -4.
- Between 10 and 5, the difference is -5.
- Between 5 and -4, the difference is -9.
- Between -4 and -13, the difference is -9.
This suggests that the sequence decreases by 9 each time. Now, let's test the formulas provided:
- Mary suggests g(n) = 14 - 9(n-1). For n=1, g(1) = 14 - 9(1-1) = 14, which matches the first term of the sequence. For n=2, g(2) = 14 - 9(2-1) = 14 - 9 = 5, which does not match the second term (should be 10).
- Alice suggests g(n) = 14 - 9n. For n=1, g(1) = 14 - 9(1) = 14 - 9 = 5, which does not match the first term of the sequence.
However, it seems there is a confusion in the application of both formulas as neither correctly matches the given sequence values for the initial terms. Therefore, the correct answer would be D. Neither Mary nor Alice.