Final answer:
The 14th term of the arithmetic sequence is 7x-9.
Step-by-step explanation:
The given arithmetic sequence is: x-4, 7x-9, 13x-14, ...
To find the 14th term of the sequence, we need to find the general formula for the nth term. We notice that the sequence has a constant difference between terms, which is 3x-5. So, the formula for the nth term is:
a = (first term) + (n-1)(common difference)
Substituting the values for the first term (x-4) and the common difference (3x-5) into the formula, we have:
a<14> = (x-4) + (14-1)(3x-5)
Simplifying:
a<14> = 7x-9
Therefore, the 14th term of the arithmetic sequence is 7x-9.