Let S be the set of all values of a_1 for whi | vedclass

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Question

let $a_1$ be any natural number

$a_1, a_1+1, a_1+2, \ldots ., a_1+99 	ext { are values of } a_i ' S$

$\bar{x}=\frac{a_1+\left(a_1+1ight)+

Vedclass · Accepted Answer

$N$

Vedclass · Answer

let $a_1$ be any natural number

$a_1, a_1+1, a_1+2, \ldots ., a_1+99 	ext { are values of } a_i ' S$

$\bar{x}=\frac{a_1+\left(a_1+1ight)+\left(a_1+2ight)+\ldots . .+a_1+99}{100}$

$=\frac{100 a_1+(1+2+\ldots . .+99)}{100}=a_1+\frac{99 	imes 100}{2 	imes 100}$

$=a_1+\frac{99}{2}$

$	ext { Mean deviation about mean }=\frac{\sum \limits_{i=1}^{100}\left|x_i-\bar{x}ight|}{100}$

$=\frac{2\left(\frac{99}{2}+\frac{97}{2}+\frac{95}{2}+\ldots .+\frac{1}{2}ight)}{100}$

$=\frac{1+3+\ldots .+99}{100}$

$=\frac{\frac{50}{2}[1+99]}{100}$

$=25$

So, it is true for every natural no. ' $a_1{ }^{\prime}$

$x_i$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
$f_i$	$4$	$4$	$\alpha$	$15$	$8$	$\beta$	$4$	$5$

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a _1, a _2, a _3, \ldots ., a _{100}$ is $25$. Then $S$ is

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