Final answer:
The formula for the geometric sequence beginning with 12, 4, and 4/3 is an = 12 × (1/3)^(n-1), with the common ratio being 1/3.
Step-by-step explanation:
The student is asking for the formula of a geometric sequence that starts with the terms 12, 4, and 4/3. To find this, we need to determine the common ratio (r). We can get the ratio by dividing the second term by the first term or the third term by the second term. So, r = 4/12 = 1/3 or r = (4/3)/4 = 1/3. With the common ratio and the first term (a1 = 12), we can write the formula for the geometric sequence as:
an = a1 × r(n-1)
Plugging in the values we have, the formula becomes:
an = 12 × (1/3)(n-1)