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

,(1 point)
Responses

a7=3
A sub 7 is equal to 3

a7=27
A sub 7 is equal to 27

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

a7=19
A sub 7 is equal to 1 ninth

1 answer

To describe the term \( a_7 \) in the given sequence \( 81, 27, 9, 3, 1, ... \), we first note that the sequence appears to be a geometric sequence where each term is obtained by dividing the previous term by 3.

The first five terms are:

  • \( a_1 = 81 \)
  • \( a_2 = 27 \)
  • \( a_3 = 9 \)
  • \( a_4 = 3 \)
  • \( a_5 = 1 \)

To find subsequent terms:

  • \( a_6 = \frac{a_5}{3} = \frac{1}{3} \)
  • \( a_7 = \frac{a_6}{3} = \frac{1/3}{3} = \frac{1}{9} \)

Now we can conclude:

\[ a_7 = \frac{1}{9} \]

Therefore, the correct choice is:

a7=19 A sub 7 is equal to 1 ninth.