Question

# If each of $$n$$ numbers $$x_i = i$$ is replaced by $$(i+1)x_i$$, then the new mean is

A
(n+1)(n+2)n
B
n+1
C
(n+1)(n+2)3
D
none of these

Solution

## The correct option is C $$\displaystyle\frac{(n+1)(n+2)}{3}$$Required mean $$=\displaystyle \frac{\sum (1+i)x_i}{n}= \frac{\sum (1+i)i}{n} =\frac{\sum (i^2+i)}{n}=\frac{\sum i^2+\sum i}{n}$$$$\displaystyle \quad =\frac{\frac{1}{6}n(n+1)(2n+1)+\frac{1}{2}n(n+1)}{n}=\frac{(n+1)(n+2)}{3}$$Mathematics

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