Insert five numbers between 1/27 and 27 to form a geometric sequence. there are 2 answers

1/27, 1/9, 1/3, 1, 3, 9, 27

27, 9, 3, 1, 1/3, 1/9, 1/27

Step-by-step explanation:

The nth term of a geometric sequence is:

aₙ = a₁ rⁿ⁻¹

If 1/27 is the first term, and 27 is the 7th term, then:

27 = 1/27 r⁷⁻¹

27 = 1/27 r⁶

27² = r⁶

27 = r³

r = 3

This sequence is 1/27, 1/9, 1/3, 1, 3, 9, 27.

On the other hand, if 27 is the first term, and 1/27 is the 7th term, then:

1/27 = 27 r⁷⁻¹

1/27 = 27 r⁶

1/27² = r⁶

1/27 = r³

r = 1/3

This sequence is 27, 9, 3, 1, 1/3, 1/9, 1/27.