Question

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

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

Answer 1

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

Mean of n terms $=\overline{x}$
Sum of n terms $=n\overline{x}$
Sum of $(n-1)$ terms $=k$
$n^{th}$ term $=$ Sum of n terms $-$ Sum of $(n-1)$ terms $=n\overline{x}-k$