Given the first five terms of the sequence 81, 27, 9, 3, 1, 1/3

Question

... use the subscript notation to describe a7
.(1 point)
Responses

a7=27
A sub 7 is equal to 27

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

a7=19
A sub 7 is equal to 1 ninth

a7=3

Answer 1

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.