# If mean of the series $$x_1$$, $$x^2$$, ….. , $$x_n$$ is $$\bar{x}$$, then the mean of the series $$x_i$$ + 2i, i = 1, 2, ……, n will be

## Solution :

As given $$\bar{x}$$ = $$x_1 + x_2 + …. + x_n\over n$$

If the mean of the series $$x_i$$ + 2i, i = 1, 2, ….., n be $$\bar{X}$$, then

$$\bar{X}$$ = $$(x_1+2) + (x_2+2.2) + (x_3+2.3) + …. + (x_n + 2.n)\over n$$

= $$x_1 + x_2 + …. + x_n\over n$$ + $$2(1+2+3+….+n)\over n$$

= $$\bar{x}$$ + $$2n(n+1)\over 2n$$

= $$\bar{x}$$ + n + 1.

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