Final answer:
The sequence is geometric with a common ratio of 3. Mustafa's formula g(n) = 4 · 3^(n-1) correctly represents the sequence starting with the first term g(1) = 4. Hence, the correct answer is b. Only Mustafa.
Step-by-step explanation:
The sequence given is geometric, where each term is obtained by multiplying the previous term by a constant factor. To find the explicit formula for the sequence 4, 12, 36, 108, ..., we examine the relationship between consecutive terms. We note that each term is 3 times the previous term (e.g., 12 is 3 times 4, 36 is 3 times 12, etc.), which suggests a common ratio of 3.
Let's check Haruka's formula: g(n) = 4 · 3^n. For n=1, g(1) = 4 · 3^1 = 4 · 3 = 12, which is not the first term of the sequence. Hence, Haruka's formula does not provide the right first term. Now, let's check Mustafa's formula: g(n) = 4 · 3^(n-1). For n=1, g(1) = 4 · 3^(1-1) = 4 · 3^0 = 4 · 1 = 4, which correctly represents the first term of the sequence. Continuing with this formula, for n=2, g(2) = 4 · 3^(2-1) = 4 · 3 = 12, and so on, which correctly generates the sequence. Therefore, the correct option here is Mustafa's formula, which accurately represents the given sequence with the first term being g(1). So the answer is b. Only Mustafa.