COMEDK · Maths · 5. Sequences and Series
If three numbers \(a, b, c\) constitute both an A.P and G.P, then
- A \(a=b-c\)
- B \(a b=c\)
- C \(a=b=c\)
- D \(a=b+c\)
Answer & Solution
Correct Answer
(C) \(a=b=c\)
Step-by-step Solution
Detailed explanation
Let the three numbers be \(a, b, c\). Since \(a, b, c\) are in A.P., we have \(2b = a + c\). Since \(a, b, c\) are in G.P., we have \(b^2 = ac\). Substituting \(c = 2b - a\) into the G.P. equation: \(b^2 = a(2b - a)\) \(b^2 = 2ab - a^2\) \(a^2 - 2ab + b^2 = 0\) \((a - b)^2 = 0\)…
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