Question

If the arithmetic mean of n numbers of a series is $\overline{x}$ and the sum of the first (n-1) numbers is k, then the nth number is

• A. n+k
• B. $n\overline{x}+k$
• C. $n\overline{x}-k$
• D. n-k

Answer 1

The correct option is C $n\overline{x}-k$

$Sum$ $of$ $all$ $the$ $n$ $numbers$ $=Mean\times no.ofnumbers=n\times \overline{x}$
$Sum$ $of$ $n-1$ $numbers$ $=k$
$Thus$ $nth$ $number$ $=n\times \overline{x}-k$