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.