Question

Mary and Alice were asked to find an explicit formula for the sequence 14, 10 points, 5, -4, -13, ... Mary said the formula is g(n)=14−9(n−1) Alice said the formula is g(n)=14−9n. Which one of them is right?

a. Only Mary
b. Only Alice
c. Both Mary and Alice
d. Neither Mary nor Alice

Answer 1

The correct formula for the given sequence is g(n)=14−9(n−1), which is Mary's solution. Alice's formula g(n)=14−9n does not yield the correct values for the sequence, which decreases by 9 for each successive term.

Step-by-step explanation:

The sequence in question is 14, 10, 5, -4, -13, and we're trying to find an explicit formula for it. To determine which formula is correct, we can analyze how the sequence progresses. Each term decreases by 9 from the previous one. Using this pattern, to calculate the nth term of the sequence (g(n)), we can take the first term (14) and subtract 9 times (n-1), because for the first term (n=1), we do not want to subtract anything. Hence Mary's formula is g(n)=14−9(n−1).

To test Alice's formula, which is g(n)=14−9n, we can substitute n=1 (the first term) and observe that it yields 14-9(1)=5, which is not the first term of the sequence. Thus, Alice's formula is incorrect and only Mary's formula accurately represents the sequence.