TS EAMCET · Maths · Statistics
Assertion (A): The variance of the first \(\mathrm{n}\) odd natural numbers is \(\frac{n^2-1}{3}\). Reason (R): The sum of the first \(\mathrm{n}\) odd natural numbers is \(\mathrm{n}^2\) and the sum of the squares of the first \(\mathrm{n}\) odd natural numbers is \(\frac{n\left(4 n^2-1\right)}{3}\). Which of the following alternatives is correct?
- A (A) and (R) are true. (R) is correct explanation of (A)
- B (A) and (R) are true, but (R) is not a correct explanation of \((\mathrm{A})\)
- C (A) is true, but (R) is false
- D (A) is false, but (R) is true
Answer & Solution
Correct Answer
(A) (A) and (R) are true. (R) is correct explanation of (A)
Step-by-step Solution
Detailed explanation
Sum of first \(n\) odd natural numbers \[ 1+3+5+\ldots . .+(2 n-1)=\frac{n}{2}(1+2 n-1)=n^2 \] Sum of squares of first \(n\) odd natural numbers…
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