Question

Insert two geometric means between 729 and 64​

Answer 1

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

$a_{n}$ = a₁$(r)^{n-1}$

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 = $\frac{64}{729}$ ( take the cube root of both sides )

r = $\sqrt[3]{\frac{64}{729} }$ = $\frac{4}{9}$ , then

a₂ = 729 × $\frac{4}{9}$ = 81 × 4 = 324

a₃ = 324 × $\frac{4}{9}$ = 36 × 4 = 144

Thus

729, 324, 144, 64