If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?

1. y² = x²z²

2. y² = x² + z²

3. y² = xz

4. xyz = 1

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

Given,

5th term = x

x = ar^{5 - 1}

x = ar⁴

8th term = y

y = ar^{8 - 1}

y = ar⁷

11th term = z

z = ar^{11 - 1}

z = ar¹⁰

Substituting value of y in L.H.S. of y² = xz

⇒ y²

⇒ (ar⁷)²

⇒ (a²r¹⁴)

Substituting value of x and z in R.H.S. of y² = xz

⇒ xz

⇒ ar⁴ × ar¹⁰

⇒ a²r¹⁴.

Since, R.H.S. = L.H.S.

Hence proved, that y² = xz.

Hence, option 3 is the correct option.