Average....Mean...Basics

Number Theory Level pending

The average of n n numbers is k k . When another number x x is added to the set, the average increases by 1 1 . The value of x x is:

k + 1 k + n + 1 k + n n

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Naren Bhandari
Aug 13, 2018

Firstly, k = ∑ n n ⟹ ∑ n = k n k =\dfrac{\sum_{}^{} n }{n}\implies \sum_{}^{}n = kn Secondly k + 1 = ∑ n + x n + 1 ⟹ x = ( k + 1 ) ( n + 1 ) − ∑ n = k + n + 1 k+ 1 =\dfrac{\sum_{}^{} n+x }{n+1 }\implies x=\,(k+1)\,(n+1) -\sum_{}^{}n =\boxed{k+n+1 }

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