The AM of $n$ numbers of a series is $¯ ¯¯¯ ¯ X$ . If the sum of first $(n - 1)$ terms is $k$ , then the $n^{t h}$ number is

¯ ¯¯¯ ¯ X - k

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n ¯ ¯¯¯ ¯ X - k

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¯ ¯¯¯ ¯ X - n k

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n ¯ ¯¯¯ ¯ X - n k

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Solution

The correct option is A $n ¯ ¯¯¯ ¯ X - k$
Let $x_{1}, x_{2}, x_{3}, . . . ., x_{n - 1}, x_{n}$ be the n terms.
Then $¯ ¯¯¯ ¯ X = \frac{x_{1} + x_{2} + . . . . + x_{n - 1} + x_{n}}{n}$
$n ¯ ¯¯¯ ¯ X = x_{1} + x_{2} + . . . . + x_{n - 1} + x_{n}$
$n ¯ ¯¯¯ ¯ X = k + x_{n}$
$\Rightarrow x_{n} = n ¯ ¯¯¯ ¯ X - k$
Hence, option 'B' is correct.

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