Question

The 3rd, 7th, and 11th terms of a G.P. are x, y, and z, respectively, then prove that y² = xz.

Answer 1

`Tn = ar^(n-1)`

T₃ = ar²

T₇ = ar⁶

T₁₁ = ar¹⁰

To prove: y² = xz

LHS ⇒ `(ar^6)^2 = a^2r^12`

RHS ⇒ (ar²) (ar¹⁰) = a²r¹²

LHS = RHS hence proved.