JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of the first three terms of a \(G.P.\) is \(S\) and their product is \(27 .\) Then all such \(S\) lie in
- A \([-3, \infty)\)
- B \((-\infty, 9]\)
- C \((-\infty,-9] \cup[3, \infty)\)
- D \((-\infty,-3] \cup[9, \infty)\)
Answer & Solution
Correct Answer
(D) \((-\infty,-3] \cup[9, \infty)\)
Step-by-step Solution
Detailed explanation
Let three terms of G.P. are \(\frac{\mathrm{a}}{\mathrm{r}}, \mathrm{a}, \mathrm{ar}\) product \(=27\) \(\Rightarrow \mathrm{a}^{3}=27 \Rightarrow \mathrm{a}=3\) \(S=\frac{3}{r}+3 r+3\) For \({r}>0\) \(\frac{\frac{3}{r}+3 r}{2} \geq \sqrt{3^{2}} \quad(\) By \(A M \geq G M)\)…
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