39) Write an explicit formula for the recursive formula, \( a_{1}=-2, a_{n}=a_{n-1}-12, n \geq 2 \) \( a_{n}= \)

To derive the explicit formula for the given recursive formula, we start with the first term \( a_1 = -2 \). Each subsequent term decreases by 12. After \( n-1 \) reductions, the explicit formula becomes \( a_n = -2 - 12(n-1) \). Simplifying this gives us \( a_n = -2 - 12n + 12 \), which can be further simplified to \( a_n = 10 - 12n \). To check our work, let’s substitute values. For \( n=1 \), \( a_1 = 10 - 12(1) = -2 \) is correct. For \( n=2 \), \( a_2 = 10 - 12(2) = -14 \), confirming our formula follows the recursive definition accurately!