COMEDK2023Evening ShiftMathematicsSequences and SeriesActual

If three numbers a, b, c constitute both an A.P and G.P, then

Options

Aa=b-c
Ba b=c
Ca=b=c
Da=b+c

Correct answer

C. a=b=c

Step-by-step solution

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 This implies a = b . Substituting a = b into 2b = a + c , we get 2b = b + c , which implies b = c . Therefore, a = b = c . Answer: a=b=c

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