Given the first five terms of the sequence 81, 27, 9, 3, 1,... use the subscript notation to describe a7

,(1 point)
Responses

a7=27
A sub 7 is equal to 27

a7=127
A sub 7 is equal to 1 over 27

a7=3
A sub 7 is equal to 3

a7=19

1 answer

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.

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