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

**Solution:**

Let G_{1} and G_{2} be two numbers between 3 and 81 such that the series 3, G_{1}, G_{2}, 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

⇒ 3r^{3} = 81

⇒ r^{3} = 27

⇒ r = 3 (considering real roots only)

Hence,

G_{1} = ar = 3 x 3 = 9

G_{2} = ar^{2} = 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

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