JEE Mains · Maths · STD 11 - 8. sequence and series
If \(\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}\) are in an \(A.P.\) and \(\log _e \mathrm{a}-\) \(\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a\) are also in an \(A.P,\) then \(a: b: c\) is equal to
- A \(9: 6: 4\)
- B \(16: 4: 1\)
- C \(25: 10: 4\)
- D \(6: 3: 2\)
Answer & Solution
Correct Answer
(A) \(9: 6: 4\)
Step-by-step Solution
Detailed explanation
\(\log _e a, \log _e b, \log _e c\) are in \( A.P.\) \(\therefore \mathrm{b}^2=\mathrm{ac}\) Also \(\log _{\circ}\left(\frac{a}{2 b}\right), \log _{\circ}\left(\frac{2 b}{3 c}\right), \log _{\circ}\left(\frac{3 c}{a}\right)\) are in \(A.P.\)…
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