The sequence given is 81, 27, 9, 3, 1,... which follows a pattern where each term is obtained by dividing the previous term by 3.
In subscript notation, we can express the terms as follows:
- \( a_1 = 81 \)
- \( a_2 = 27 \)
- \( a_3 = 9 \)
- \( a_4 = 3 \)
- \( a_5 = 1 \)
The nth term of the sequence can be represented as: \[ a_n = \frac{81}{3^{n-1}} \]
To find \( a_7 \): \[ a_7 = \frac{81}{3^{7-1}} = \frac{81}{3^6} = \frac{81}{729} = \frac{1}{9} \]
However, none of the answers directly match \( \frac{1}{9} \). Let's analyze the responses given:
- a7=27 → False, since \( a_2 = 27 \)
- a7=127 → False, since \( a_7 \) is not \( \frac{1}{27} \).
- a7=3 → False, since \( a_4 = 3 \)
- a7=19 → False.
Given the derived formula, we see none of the options are correct.
Thus, the answer based on the expected choices is not available and we need to identify that \( a_7 = \frac{1}{9} \). Please check the options provided again for accuracy.
1 answer