To find the explicit formula for the given sequence, we first need to observe the pattern of the sequence. The given sequence is:

$1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots$

From this sequence, we can see that the general term for the $n$-th term of the sequence can be written as:

$a_n = \frac{1}{n}$

Thus, the explicit formula for the $n$-th term of the sequence is:

$a_n = \frac{1}{n}$

Do you want details or have any questions?

Here are some related questions for further exploration:

1. What is the sum of the first $n$ terms of this sequence?
2. How does the harmonic series, related to this sequence, behave as $n$ approaches infinity?
3. What is the partial sum of the first $10$ terms of this sequence?
4. How can this sequence be represented graphically?
5. What is the difference between the $n$-th term and the $(n+1)$-th term?
6. How can you derive the $n$-th term of this sequence using the concept of limits?
7. What is the significance of the harmonic series in mathematical analysis?
8. Can you find another sequence with a similar pattern but different initial terms?

Tip:

When working with sequences, identifying the pattern or relationship between consecutive terms can often help in determining the explicit formula.