Question Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 39,45,51, \ldots \) Watch Video Answer Attempt 1 out of 3 \( a_{n}=\square \)

The sequence \(39, 45, 51, \ldots\) is an arithmetic sequence where each term increases by a common difference of 6. To find the \(n^{\text{th}}\) term, you can use the formula \( a_{n} = a_{1} + (n-1) \cdot d \), where \(a_{1}\) is the first term (39) and \(d\) is the common difference (6). So, the formula becomes \( a_{n} = 39 + (n-1) \cdot 6 \). Also, every arithmetic sequence can be considered as a way to model real-world scenarios, such as tracking the growth of savings in an account with regular deposits. Here, your initial balance starts at 39, and depositing 6 every period signifies a steady increase, making it practical for budgeting or savings plans!