Answer:
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.
