JEE Mains · Maths · STD 11 - 8. sequence and series
Three positive numbers form an increasing \(G.P.\) If the middle term in this \(G.P.\) is doubled, the new numbers are in \(A.P.\) then the common ratio of the \(G.P.\) is:
- A \(2 - \sqrt 3 \)
- B \(2 + \surd 3\)
- C \(\sqrt 2 + \surd 3\)
- D \(3 + \surd 2\)
Answer & Solution
Correct Answer
(B) \(2 + \surd 3\)
Step-by-step Solution
Detailed explanation
Let the numbers be \(a, a r, a r^{2}\) If \(a r\) is doubled then, \(\Longrightarrow 2 a r=\frac{a r^{2}+a}{2}\) \(\Longrightarrow 4 a r=a r^{2}+a\) \(\Longrightarrow 4 r=r^{2}+1\) \(\Longrightarrow r^{2}-4 r+1\) On solving we get \(r=2 \pm \sqrt{3}\) since it is an increasing…
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