Write the first 5 terms of the arithmetic sequence, given the first term and the common difference.
(B) $a_1=\frac{3}{2}$; $d=\frac{1}{4}$

• A. $\frac32,1,\frac12,0,-\frac12$
• B. $\frac32,\frac54,1,\frac34,\frac12$
• C. $\frac32,\frac74,2,\frac94,\frac52$
• D. $\frac32,2,\frac52,3,\frac72$

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. 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: \(S_n = \frac{n}{2} (2a_1 + (n - 1)d)\).