Question

(a) Insert 3 geometric m4earns between 1/9 and 9 . (b) if a, ar,ar^2, ar^3.... Be in G.P. find the. Common ratio.

Answer 1

Step-by-step explanation:

(a)

Let a₁,a₂,a₃ be 3 geometric means between (1/9) and 9.

The Sequence will be (1/9), a₁, a₂, a₃, 9 are in G.P.

Here, a = (1/9).

Now,

⇒ 9 = (1/9) * r⁴

⇒ 3² = 3⁻² * r⁴

⇒ 3⁴ = r⁴

⇒ r = 3

Then,

a₁ = (1/9)

a₂ = ar = (1/3)

a₃ = ar² = 1

a₄ = ar³ = 3

a₅ = ar⁴ = 9.

Hence (1/3), 1,9 are the three geometric means.

(b)

The general form of the G.P is a, ar, ar², ar³.

Here,

a is called as the first term.

r is called as common ratio.

Hope it helps