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. $\frac{3}{2},1,\frac{1}{2},0,-\frac{1}{2}$
• B. $\frac{3}{2},\frac{5}{4},1,\frac{3}{4},\frac{1}{2}$
• C. $\frac{3}{2},\frac{7}{4},2,\frac{9}{4},\frac{5}{2}$
• D. $\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}$

Answer: (C)

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 write an expression for the nth term of the sequence.
5. If asked to find a specific term or sum of terms, substitute the given value of \(n\) into the formula or use the sum formula for arithmetic sequences: \(S_n = \frac{n}{2} (a_1 + a_n)\).