Final answer:
To find the explicit formula for the sequence g(n) = g(n-1) + 6, we can start with the initial value g(1) = -19 and add 6 to each previous term to find subsequent terms. The explicit formula for g(n) is g(n) = -19 + 6(n-1), which can be simplified to g(n) = -13 + 6n.
Step-by-step explanation:
To find an explicit formula for the sequence g(n) = g(n-1) + 6, we need to first determine an initial value for g(1). In the given question, it is stated that g(1) = -19. Using this initial value, we can then determine the explicit formula for g(n).
Starting with g(1) = -19, we can find g(2), g(3), and so on, by adding 6 to the previous term: g(2) = g(1) + 6 = -19 + 6 = -13. Similarly, g(3) = g(2) + 6 = -13 + 6 = -7.
This pattern continues, with each term being 6 more than the previous term. Therefore, the explicit formula for g(n) is g(n) = -19 + 6(n-1). This can also be simplified to g(n) = -13 + 6n.