KCET · Maths · Sequences and Series
If \(4^{\text {th }}, 10^{\text {th }}\) and \(16^{\text {th }}\) terms of a G.P. are \(\mathrm{x}, \mathrm{y}\) and z respectively, then
- A \(z=\sqrt{x y}\)
- B \(y=\sqrt{x z}\)
- C \(x=\sqrt{y z}\)
- D \(y=\frac{x+z}{2}\)
Answer & Solution
Correct Answer
(B) \(y=\sqrt{x z}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}x=a r^3 & \\ y=a r^9 & x z=a^2 x^{18}=\left(a r^9\right)^2 \\ z=a r^{15} & \Rightarrow y^2=x z \Rightarrow y=\sqrt{x z}\end{array}\)
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