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Question

The weighted mean of first n natural numbers whose weights are equal to the corresponding number is equal to

A
13(2n+1)
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B
12(n+4)
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C
15(2n+3)
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D
None of these
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Solution

The correct option is A 13(2n+1)
xi1,2,3,4...n
Similarily weight is
fi1,2,3,4,...,n respectively
Weighted AM=f1x1+f2x2+f3x3+.....+fnxnf1+f2+f3+.....+fn=(1×1)+(2×2)+(3×3)+....+(n×n)1+2+3+4+...+n=nk=1k2nk=1k=n(n+1)(2n+1)6n(n+1)2=2n+13

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