Final answer:
To find the common ratio of the given series 1/3 + 1/6 + 1/9 + ..., we divide the second term by the first term, resulting in 1/2. Thus, the correct answer is option a) 1/2.
Step-by-step explanation:
The student is asking about the common ratio of a series 1/3 + 1/6 + 1/9 + .... This type of series, where you multiply a term by a constant to get the next term, is known as a geometric series.
To find the common ratio, we divide a term in the series by the term that comes just before it. This is done by dividing 1/6 (the second term) by 1/3 (the first term), resulting in (1/6) / (1/3) = (1/6) * (3/1) = 1/2. Therefore, the common ratio is 1/2. So, the correct answer here is option a) 1/2, which you would mention as the correct option in the final answer when explaining geometric series and common ratios to the student.