Incert Two Geometric Means Between 8 And 27

Incert two geometric means between 8 and 27

 

Answer:

The two geometric means are 12 and 18.

Step-by-step explanation:

Given:

a₁ = 8

an or a₄ = 27

n = 4

Since two geometric means are required, there are 4 terms in the given sequence:

8, a₂, a₃, 27

Where a₂ and a₃ are the two geometric means.

Find the common ratio, r:

an = a₁(r)ⁿ⁻¹  ⇒  the geometric sequence general rule

27 = 8(r)⁴⁻¹

27 = 8(r)³

r³ = 27/8

∛(r³) = ∛(27/8)

r = 3/2

Find a₂:

a₂ = (a₁)(r)

a₂ = (8)(3/2)

a₂ = 12

Find a₃:

a₃ = (a₂)(r)

a₃ = 12 (3/2)

a₃ = 18

Check if a₄=27:

a₄ = (a₃)(r)

27 = (18)(3/2)

27 = ()(3)

27 = 27  (True)

The two geometric means are 12 and 18.

The geometric sequence is 8, 12, 18, 27.