TS EAMCET · Maths · 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, that, \(2 b=a+c\) and \((c-b)^2=(b-a) a\) \(\begin{aligned} & \therefore \quad(b-a)^2=(b-a) a \\ & \Rightarrow \quad b=2 a \\ & \Rightarrow \quad c=3 a \\ & \Rightarrow \quad a: b: c=1: 2: 3 \\ & \end{aligned}\)
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