Answer:
The geometric means between 2 and 81/8 are 3, 9/2, 27/4.
Thus, the sequence becomes 2, 3, 9/2, 27/4, 81/8.
Step-by-step explanation:
Find the common ratio using the formula an=a1•r^n-1
an=a1•r^n-1
a5=a1•r^4
81/8=2r^4
(Divide both sides by 2)
81/16=r^4
Take the root of both sides and use positive and negative roots.
(See the solution on how to get the root in the picture)
Therefore the common ratio or r is 3/2.
Solve now for a2, a3, a4.
an=a1•r^n-1
a2= 2(3/2)^1
a2=3
an=a1•r^n-1
a3=2(3/2)^2
a3=2(9/4)
a3=18/4
a3=9/2
an=a1•r^n-1
a4=2(3/2)^3
a4=2(27/8)
a4=54/8
a4=27/4
