The problem is asking for the formula of the $n$-th term of the arithmetic sequence $-1, 1, 3, 5, \dots$.

To solve this, we need to recognize that an arithmetic sequence follows the pattern:

$U_n = a + (n-1) \cdot d$

where:

• $U_n$ is the $n$-th term,
• $a$ is the first term of the sequence,
• $d$ is the common difference between consecutive terms,
• $n$ is the term number.

Step 1: Identify the first term $a$ and the common difference $d$

• The first term $a = -1$.
• The common difference $d = 1 - (-1) = 2$.

Step 2: Substitute the values into the formula

$U_n = -1 + (n-1) \cdot 2$ Simplifying: $U_n = -1 + 2n - 2$ $U_n = 2n - 3$

Conclusion:

The formula for the $n$-th term of this arithmetic sequence is $U_n = 2n - 3$, which corresponds to option C.

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:

1. How do you determine the common difference in an arithmetic sequence?
2. What is the general formula for the sum of the first $n$ terms of an arithmetic sequence?
3. How do arithmetic sequences differ from geometric sequences?
4. Can an arithmetic sequence have a common difference of 0?
5. What is the significance of the first term $a$ in determining the pattern of a sequence?

Tip: Always check for the common difference first when identifying the pattern in arithmetic sequences!