To understand the pattern of the given sequence \(81, 27, 9, 3, 1, \frac{1}{3}\), we can observe that each term is obtained by dividing the previous term by 3.
Here's the breakdown:
- \( a_1 = 81 \)
- \( a_2 = \frac{81}{3} = 27 \)
- \( a_3 = \frac{27}{3} = 9 \)
- \( a_4 = \frac{9}{3} = 3 \)
- \( a_5 = \frac{3}{3} = 1 \)
- \( a_6 = \frac{1}{3} = \frac{1}{3} \)
Continuing this pattern, we find \( a_7 \):
- \( a_7 = \frac{a_6}{3} = \frac{1/3}{3} = \frac{1}{9} \)
So, in subscript notation:
\[ a_7 = \frac{1}{9} \]
From the provided responses, it seems like the intended answer is:
A sub 7 is equal to 1 ninth.