Insert two numbers between 3 and 81 so that the resulting sequence is G.P

Solution:

Let G₁ and G₂ be two numbers between 3 and 81 such that the series 3, G₁, G₂, 81 forms a G.P.

Let a be the first term and r be the common ratio of the G.P.

Therefore, a = 3 and a4 = 81

⇒ 3r³ = 81

⇒ r³ = 27

⇒ r = 3 (considering real roots only)

Hence,

G₁ = ar = 3 x 3 = 9

G₂ = ar² = 3 x (3)² = 27

Thus, the required two numbers are 9 and 27

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 26

Insert two numbers between 3 and 81 so that the resulting sequence is G.P

Summary:

Therefore, the two numbers to be inserted between 3 and 81 so that the resulting sequence is G.P are 9 and 27