A) \[\bar{x}+2n\]
B) \[\bar{x}+n+1\]
C) \[\bar{x}+2\]
D) \[\bar{x}+n\]
Correct Answer: B
Solution :
We know that \[\bar{x}=\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n}\] i.e., \[\sum\limits_{i=1}^{n}{{{x}_{i}}}=n\bar{x}\] \ \[\frac{\sum\limits_{i=1}^{n}{({{x}_{i}}+2i)}}{n}=\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}+2\sum\limits_{i=1}^{n}{i}}{n}=\frac{n\bar{x}+2(1+2+...n)}{n}=\frac{n\bar{x}+2\frac{n(n+1)}{2}}{n}=\bar{x}+(n+1)\] \[=\frac{n\bar{x}+2\frac{n(n+1)}{2}}{n}=\bar{x}+n+1\].
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