Question

H(n) = –15 · 6ⁿ
Complete the recursive formula of h(n).

Answer 1

The recursive formula for h(n) = -15 · 6^n is h(0) = -15 and h(n) = 6 · h(n-1) for n >= 1.

Step-by-step explanation:

The question asks for the completion of the recursive formula for the function h(n) = −15 · 6n. To create a recursive formula, we need to express h(n) in terms of h(n-1).

Starting with the given function:

• h(n) = −15 · 6n
• h(n-1) = −15 · 6n−1

To define h(n) recursively, we look at the relationship between h(n) and h(n-1). We can see that h(n) is simply h(n-1) multiplied by 6:

• h(n) = 6 · h(n−1), for n ≥ 1

Initial condition:

• h(0) = −15, because 60 = 1, and −15 · 1 = −15

So the complete recursive formula is:

• h(0) = −15
• h(n) = 6 · h(n−1), for n ≥ 1