Question

The arithmetic mean of a-3d, a- d, a+d and a + 3d is

• A. a
• B. d
• C. 2a
• D. 2d

Answer 1

The Correct Option is A

Correct answer: a 

Explanation:
The arithmetic mean of a set of numbers is given by the sum of the numbers divided by the number of terms. Here, the terms are \(a - 3d\), \(a - d\), \(a + d\), and \(a + 3d\). The arithmetic mean is: \[ \text{Mean} = \frac{(a - 3d) + (a - d) + (a + d) + (a + 3d)}{4} \] Simplifying the numerator: \[ (a - 3d) + (a - d) + (a + d) + (a + 3d) = 4a \] So, the arithmetic mean is: \[ \text{Mean} = \frac{4a}{4} = a \]

Hence, the arithmetic mean is a.