Find the common difference of the following sequence.
(A) $-9,-4,1,6,\dots$

• A. $4$
• B. $-4$
• C. $-5$
• D. $5$

Answer: (A)

Verified step by step guidance

1. Understand that an arithmetic sequence is a list of numbers where the difference between consecutive terms is constant. This difference is called the common difference, denoted as \(d\).
2. Identify the first term of the sequence, denoted as \(a_1\). This is the starting point of the sequence.
3. Use the formula for the \(n\)-th term of an arithmetic sequence: \(a_n = a_1 + (n - 1) \times d\). This formula helps find any term in the sequence.
4. If the problem asks for the sum of the first \(n\) terms, use the sum formula: \(S_n = \frac{n}{2} \times (2a_1 + (n - 1) \times d)\), where \(S_n\) is the sum of the first \(n\) terms.
5. Apply the given values from the problem into these formulas step-by-step to find the required term or sum, making sure to substitute correctly and simplify carefully.