JEE Mains · Maths · STD 11 - 8. sequence and series
If the variance of the terms in an increasing \(A.P.\), \(b _{1}, b _{2}, b _{3}, \ldots b _{11}\) is \(90,\) then the common difference of this \(A.P.\) is
- A \(3\)
- B \(9\)
- C \(-9\)
- D \(-3\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
Let a be the first term and \(d\) be the common difference of the given A.P. Where \(d>0\) \(\overline{ X }= a +\frac{0+ d +2 d +\ldots+10 d }{11}\) \(=a+5 d\) \(\Rightarrow\) varience \(=\frac{\Sigma\left(\bar{X}-x_{i}\right)^{2}}{11}\)…
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