What is the value of the term being asked for?
$a_n=\frac{2n+1}{n+4}$
$a_4=?$

• A. $\frac{11}{9}$
• B. $\frac{5}{6}$
• C. $1$
• D. $\frac{9}{8}$

Answer: (D)

Verified step by step guidance

1. Identify the type of sequence you are working with. Common types include arithmetic sequences (where each term increases by a constant difference) and geometric sequences (where each term is multiplied by a constant ratio).
2. If the sequence is arithmetic, find the common difference \(d\) by subtracting the first term from the second term: \(d = a_2 - a_1\). If the sequence is geometric, find the common ratio \(r\) by dividing the second term by the first term: \(r = \frac{a_2}{a_1}\).
3. Write the general formula for the \(n\)-th term of the sequence. For an arithmetic sequence, use \(a_n = a_1 + (n - 1)d\). For a geometric sequence, use \(a_n = a_1 \times r^{n-1}\).
4. Use the general formula to find any term in the sequence by substituting the value of \(n\) (the term number) into the formula.
5. If the problem asks for the sum of the first \(n\) terms, use the appropriate sum formula: for arithmetic sequences, \(S_n = \frac{n}{2} (2a_1 + (n - 1)d)\); for geometric sequences, if \(r \neq 1\), \(S_n = a_1 \frac{1 - r^n}{1 - r}\).