WBJEE · Maths · Sequences and Series
If the first and \((2 n-1)\) th terms of an \(\mathrm{AP}\), GP and \(\mathrm{HP}\) are equal and their \(n\) th terms are respectively \(a, b, c,\) then always
- A \(a=b=c\)
- B \(a \geq b \geq c\)
- C \(a+c=b\)
- D \(a c-b^{2}=0\)
Answer & Solution
Correct Answer
(D) \(a c-b^{2}=0\)
Step-by-step Solution
Detailed explanation
\(\because a, b\) and \(c\) are respectively the \(A M,\) GM and HM of first and \((2 n-1)\) th terms. and also, we know \(A M \geq G M \geq H M\) and \(A M \cdot H M=G M^{2}\) \(\therefore \quad a \geq b \geq c\) and \(a \cdot c=b^{2}\)
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