Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 39,31,23, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \)

To find the explicit formula for the \( n^{\text{th}} \) term of the sequence \( 39, 31, 23, \ldots \), we first look for a pattern in the numbers. The differences between consecutive terms are: - \( 31 - 39 = -8 \) - \( 23 - 31 = -8 \) The sequence decreases by 8 each time, which indicates it is an arithmetic sequence with a common difference of \(-8\). The formula for the \( n^{\text{th}} \) term of an arithmetic sequence is given by: \[ a_n = a_1 + (n-1) \cdot d \] Where \( a_1 \) is the first term and \( d \) is the common difference. Thus: - \( a_1 = 39 \) - \( d = -8 \) Plugging in these values, we get: \[ a_n = 39 + (n-1)(-8) \] \[ a_n = 39 - 8(n-1) \] \[ a_n = 39 - 8n + 8 \] \[ a_n = 47 - 8n \] So, the explicit formula for the \( n^{\text{th}} \) term is: \[ \boxed{a_n = 47 - 8n} \]