Determine the Increment Pattern: From -4 to -1 in the Sequence

To solve this sequence problem, we will use the following steps:

• Step 1: Identify the difference between the successive terms.
• Step 2: Use the common difference to find the term-to-term rule.
• Step 3: Verify the rule with the provided terms.

Let's go through each step:
Step 1: The sequence given is $-4, -3, -2, -1$. The difference between each successive pair of terms is $+1$ (e.g., $-3 - (-4) = 1$, $-2 - (-3) = 1$).
Step 2: Since the common difference $d$ is $1$, this indicates the sequence is arithmetic and increases by 1 for each subsequent term. To form the term-to-term rule, we note that each term is calculated by adding 1 to the previous term.
Step 3: To express this rule in formula terms, consider $n$ as the number of the term, where $n = 1$ corresponds to the first term. The first term is $-4$. By analyzing the sequence further, a formula aligning with these steps is $a_n = n - 5$ for the given terms (-4, -3, -2, -1). Substituting into this formula, for $n=1, 2, 3, 4$, we obtain $-4, -3, -2, -1$ respectively.

Therefore, the term-to-term rule for the given sequence is $n-5$.