TS EAMCET · Maths · Sequences and Series
If the variance of the numbers \(9,15,21, \ldots .,(6 n+3)\) is P, then the variance of the first \(n\) even numbers is
- A 9P
- B 3 P
- C \(\frac{P}{9}\)
- D \(\frac{P}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{P}{9}\)
Step-by-step Solution
Detailed explanation
Let the given sequence be \(x_i = 6i+3\) for \(i=1, \ldots, n\). Given \(Var(x_i) = P\). \(P = Var(6i+3) = 6^2 Var(i) = 36 Var(i)\). \(Var(i) = \frac{P}{36}\). The first \(n\) even numbers are \(e_i = 2i\) for \(i=1, \ldots, n\). \(Var(e_i) = Var(2i) = 2^2 Var(i)\).…
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