Write a general formula for the arithmetic sequence given.
(A) $-5,-12,-19,-26,\dots$

• A. $a_{n}=7n-12$
• B. $a_{n}=-7n+2$
• C. $a_{n}=7n+2$
• D. $a_{n}=-7n-12$

Answer: (B)

Verified step by step guidance

1. Identify the general form of an arithmetic sequence, which is given by the formula: \(a_n = a_1 + (n - 1)d\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
2. Determine the first term \(a_1\) of the sequence from the given information or problem statement.
3. Find the common difference \(d\) by subtracting the first term from the second term, i.e., \(d = a_2 - a_1\).
4. Use the formula \(a_n = a_1 + (n - 1)d\) to express the nth term of the sequence, substituting the known values of \(a_1\) and \(d\).
5. If asked to find a specific term or sum, plug in the value of \(n\) into the formula or use the sum formula for arithmetic sequences: \(S_n = \frac{n}{2} (2a_1 + (n - 1)d)\).