Answer:
324 and 144
Step-by-step explanation:
We require
a₁, a₂, a₃, a₄
where a₂ and a₃ are the required geometric means
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 729 and a₄ = 64, thus
729(r³) = 64 ( divide both sides by 729 )
r³ = [tex]\frac{64}{729}[/tex] ( take the cube root of both sides )
r = [tex]\sqrt[3]{\frac{64}{729} }[/tex] = [tex]\frac{4}{9}[/tex] , then
a₂ = 729 × [tex]\frac{4}{9}[/tex] = 81 × 4 = 324
a₃ = 324 × [tex]\frac{4}{9}[/tex] = 36 × 4 = 144
Thus
729, 324, 144, 64
