Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 23,27,31, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \)

To find the explicit formula for the \( n^{\text{th}} \) term of the sequence \( 23, 27, 31, \ldots \), we first observe that this is an arithmetic sequence. The first term \( a_1 = 23 \) and the common difference \( d = 27 - 23 = 4 \). The formula for the \( n^{\text{th}} \) term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the known values gives us: \[ a_n = 23 + (n - 1) \cdot 4 \] Simplifying this, \[ a_n = 23 + 4n - 4 = 4n + 19 \] So, the explicit formula for \( a_n \) is: \[ a_n = 4n + 19 \]