Write the first 5 terms of the arithmetic sequence, given the first term and the common difference.
(A) $a_1=-12$; $d=-5$

• A. $-12,-17,-22,-27,-32$
• B. $-32,-27,-22,-17,-12$
• C. $-12,-7,-2,3,8$
• D. $8,3,-2,-7,-12$

Answer: (A)

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. To find a specific term or sum of terms, substitute the desired value of \(n\) into the formula or use the sum formula for arithmetic sequences: \(S_n = \frac{n}{2} (2a_1 + (n - 1)d)\).