If the 4^th, 10^th and 16^th terms of a G.P are x, y and z respectively. Prove that x, y, z are in G.P

Solution:

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

According to the given statement,

a = ar³ = x ....(1)

a₁₀ = ar⁹ = y ....(2)

a₁₆ = ar¹⁵ = z ....(3)

Dividing (2) by (1), we obtain

⇒ y/x = ar⁹/ar³

⇒ y/x = r⁶

Dividing (3) by (2), we obtain

⇒ z/y = ar¹⁵/ar⁹

⇒ z/y = r⁶

Hence,

y/x = z/y

⇒ y² = xz

⇒ y = √xz

Thus, x, y, z are in G.P, proved

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 17

If the 4^th, 10^th and 16^th terms of a G.P are x, y and z respectively. Prove that x, y, z are in G.P.

Summary:

We are given that the 4th, 10th and 16th terms in the G.P are x, y, z. We proved that they are in G.P