Find the indicated term of each arithmetic sequence.
(B) $a_n=\frac{5}{2}+\frac{3(n-1)}{4}$
Find $a_6$.

• A. $\frac{25}{4}$
• B. $5$
• C. $10$
• D. $\frac{25}{2}$

Answer: (A)

Verified step by step guidance

1. Identify the first term of the arithmetic sequence, usually denoted as \(a_1\). This is the starting value of the sequence.
2. Determine the common difference \(d\) of the arithmetic sequence. This is the constant amount added to each term to get the next term.
3. Recall the formula for the general term (also called the \(n\)th term) of an arithmetic sequence: \[a_n = a_1 + (n - 1) \times d\]
4. Substitute the known values of \(a_1\) and \(d\) into the formula to express \(a_n\) in terms of \(n\).
5. Simplify the expression if possible to get the general term formula that can be used to find any term in the sequence.