COMEDK · Maths · 5. Sequences and Series
If \(a, b, c\) are in AP, \(b-a, c-b\) and \(a\) are in GP, then \(a: b: c\) is
- A \(1: 2: 3\)
- B \(1: 3: 5\)
- C \(2: 3: 4\)
- D \(1: 2: 4\)
Answer & Solution
Correct Answer
(A) \(1: 2: 3\)
Step-by-step Solution
Detailed explanation
Given \(a, b, c\) are in AP, we have \(2b = a + c\). Let the common difference be \(d\), so \(b = a + d\) and \(c = a + 2d\). The terms \(b - a, c - b, a\) are in GP. Substituting the expressions in terms of \(a\) and \(d\): \(b - a = (a + d) - a = d\)…
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