JEE Mains · Maths · STD 11 - 8. sequence and series
If the arithmetic mean and geometric mean of the \(p ^{\text {th }}\) and \(q ^{\text {th }}\) terms of the sequence \(-16,8,-4,2, \ldots\) satisfy the equation \(4 x^{2}-9 x+5=0,\) then \(p+q\) is equal to ..... .
- A \(16\)
- B \(8\)
- C \(10\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(10\)
Step-by-step Solution
Detailed explanation
\(4 x^{2}-9 x+5=0 \Rightarrow x=1, \frac{5}{4}\) Now given \(\frac{5}{4}=\frac{ t _{ p }+ t _{ q }}{2}, t = t _{ p } t _{ q }\) where \(t _{ r }=-16\left(-\frac{1}{2}\right)^{ r -1}\) so…
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