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# 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 = ar^{3} = x ....(1)

a_{10} = ar^{9} = y ....(2)

a_{16} = ar^{15} = z ....(3)

Dividing (2) by (1), we obtain

⇒ y/x = ar^{9}/ar^{3}

⇒ y/x = r^{6}

Dividing (3) by (2), we obtain

⇒ z/y = ar^{15}/ar^{9}

⇒ z/y = r^{6}

Hence,

y/x = z/y

⇒ y^{2} = 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

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