AP EAMCET · Maths · Sequences and Series
Let \(A, G, H\) and \(S\) respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers \(a_1, a_2, a_3, \ldots, a_n\). Then the value of \(x\) at which the function \(f(x)=\sum_{k=1}^n\left(x-a_k\right)^2\) has minimum is
- A \(S\)
- B \(\mathrm{H}\)
- C \(G\)
- D \(A\)
Answer & Solution
Correct Answer
(D) \(A\)
Step-by-step Solution
Detailed explanation
Given function \(f(x)=\sum_{k=1}^n\left(x-a_k\right)^2\) \(=\sum_{k=1}^n\left(x^2-2 x a_k+a_k^2\right)\) \(\begin{aligned} & =n x^2-2 x\left(a_1+a_2+a_3+\ldots a_n\right) \\ & +\left(a_1^2+a_2^2+\ldots+a_n^2\right) \end{aligned}\) \(\because\) The quadratic expression…
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The correct match of List-I to List-II
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