COMEDK · Maths · 5. Sequences and Series
Given \(a, b, c\) are three unequal numbers such that \(\mathrm{b}\) is arithmetic mean of \(a\) and \(c\) and \((b-a),(c-b), a\) are in geometric progression. Then \(a: b: c\) is
- A \(1: 3: 5\)
- B \(2: 3: 5\)
- C \(1: 2: 3\)
- D \(1: 2: 4\)
Answer & Solution
Correct Answer
(C) \(1: 2: 3\)
Step-by-step Solution
Detailed explanation
Given that \(b\) is the arithmetic mean of \(a\) and \(c\), we have \(b = \dfrac{a+c}{2}\), which implies \(2b = a+c\) or \(c = 2b - a\). The terms \((b-a), (c-b), a\) are in geometric progression. Therefore, \((c-b)^2 = (b-a) \times a\). Substituting \(c = 2b - a\) into the…
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