Question

The arithmetic mean of n number series is $\bar{x}$. The sum of last n-1 numbers is k. Then the first number will be:

• A. 1
• B. $n\bar{x} - k$
• C. (n-1) $\bar{x}$ - k
• D. k

Hint:

To test this algebraic relationship, plug in simple numbers:
- Let the series be \(\{2, 4, 6\}\). Here, \(n=3\).
- Mean \(\bar{x} = (2+4+6)/3 = 4\).
- Sum of the last \(n-1\) numbers (4 and 6) is \(k = 10\).
- Calculate the first number: \(n\bar{x} - k = (3 \times 4) - 10 = 12 - 10 = 2\).
This matches our first number, confirming the formula works.

Answer 1

The Correct Option is B