Verified Solution • 2025–26 Session moderate

QJEEM22Ma5568: JEE Main 2022 Mathematics - Class 11 JEEM22Ma5568 Solution: If the mean deviation about the mean of the numbers 1, 2, 3,…

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is 5(n+1)n{{5(n + 1)} \over n} , then n is equal to ______________.

Step-by-Step Verified Solution

Mean =n(n+1)2n=n+12= {{n{{(n + 1)} \over 2}} \over n} = {{n + 1} \over 2}

M.D. =2(n−12+n−32+n−52+   ...   0)n=5(n+1)n= {{2\left( {{{n - 1} \over 2} + {{n - 3} \over 2} + {{n - 5} \over 2} + \,\,\,...\,\,\,0} \right)} \over n} = {{5(n + 1)} \over n}

⇒((n−1)+(n−3)+(n−5)+  ...  0)=5(n+1)\Rightarrow ((n - 1) + (n - 3) + (n - 5) + \,\,...\,\,0) = 5(n + 1)

⇒(n+14) . (n−1)=5(n+1)\Rightarrow \left( {{{n + 1} \over 4}} \right)\,.\,(n - 1) = 5(n + 1)

So, n=21n = 21

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