To determine \( a_7 \) for the sequence given (81, 27, 9, 3, 1...), we first need to identify the pattern.
The sequence can be observed as follows:
- \( a_1 = 81 \)
- \( a_2 = 27 = \frac{81}{3} \)
- \( a_3 = 9 = \frac{27}{3} \)
- \( a_4 = 3 = \frac{9}{3} \)
- \( a_5 = 1 = \frac{3}{3} \)
From this, we can see that each term is obtained by dividing the previous term by 3. Therefore, the general term can be expressed as:
\[ a_n = \frac{81}{3^{n-1}} \]
Now, we want to find \( a_7 \):
\[ a_7 = \frac{81}{3^{7-1}} = \frac{81}{3^6} \]
Since \( 81 = 3^4 \):
\[ a_7 = \frac{3^4}{3^6} = \frac{1}{3^{6-4}} = \frac{1}{3^2} = \frac{1}{9} \]
Thus, \( a_7 = \frac{1}{9} \).
So the correct response is:
A sub 7 is equal to 1 ninth.
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