Question
Download Solution PDFThe mean of n observations
1, 4, 9, 16 ...., n2 is 130. What is the value of n?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Mean = \(\frac{1+ 4+ 9 ... n^2}{n}\)
⇒ 130 = \(\frac{(n(n+1)(2n+1)}{6n}\)
⇒ 780 = 2n2 + 3n + 1
⇒ 2n2 + 3n – 779 =0
⇒ 2n2 + 41n – 38n – 779 = 0
⇒ n(2n + 41) – 19(2n + 41) = 0
⇒ (2n + 41) (n – 19) = 0
⇒ x = 19 ..... ( n = \(-\frac{41}{2}\) is not possible)
∴ Option (b) is correct.
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