The given sequence is:

$\frac{4}{7}, \frac{5}{8}, \frac{6}{9}, \dots$

We can observe the general pattern of both the numerator and denominator:

1. Numerator: The numerators are $4, 5, 6, \dots$, which follow the pattern $4 + (n-1)$. This simplifies to $3 + n$.

2. Denominator: The denominators are $7, 8, 9, \dots$, which follow the pattern $7 + (n-1)$. This simplifies to $6 + n$.

Thus, the nth term of the sequence is:

$a_n = \frac{3 + n}{6 + n}$

This is the formula for the nth term of the sequence.

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Would you like further details or have any questions about this? Here are some related questions you might find useful:

1. How do I find the nth term of a sequence where the terms increase by a constant amount?
2. How can I determine if a sequence is arithmetic or geometric?
3. How can I find the sum of the first n terms of an arithmetic sequence?
4. How do I simplify fractions involving polynomials?
5. Can this type of sequence have a limit as n approaches infinity?

Tip: To identify patterns in sequences, look at how the numerators and denominators change separately, then try to express them in terms of $n$.