What is the next term in the geometric sequence $9,3,1,\frac{1}{3},...$ ?

• A. $\frac{1}{6}$
• B. $\frac{2}{3}$
• C. $\frac{1}{9}$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Identify that the given sequence is geometric, meaning each term is found by multiplying the previous term by a constant ratio.
2. Calculate the common ratio \( r \) by dividing the second term by the first term: \( r = \frac{3}{9} \).
3. Verify the common ratio by checking if multiplying the second term by \( r \) gives the third term, and so on, to ensure the sequence is geometric.
4. Use the common ratio \( r \) to find the next term by multiplying the last given term \( \frac{1}{3} \) by \( r \): \( \text{next term} = \frac{1}{3} \times r \).
5. Express the next term as a simplified fraction or decimal, depending on the form of the previous terms.