JEE Mains · Maths · STD 11 - 8. sequence and series
If three successive terms of a\(G.P.\) with common ratio \(r(r>1)\) are the lengths of the sides of a triangle and \([\mathrm{r}]\) denotes the greatest integer less than or equal to \(r\), then \(3[r]+[-r]\) is equal to :
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\text { a, ar, } a r^2 \rightarrow \text { G.P. }\) Sum of any two sides \(>\) third side \( a+a r>a r^2, a+a r^2>a r, a r+a r^2>a \) \( r^2-r-1<0 \) \( r \in\left(\frac{1-\sqrt{5}}{2}, \frac{1+\sqrt{5}}{2}\right) \) \( r^2-r+1>0\) \(............(1)\) always true…
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