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What is the average absolute deviation from the mean for the arithmetic progression a, a + d, a + 2d,..., a + 2nd?

1. n(n + 1)d
2. n(n + 1)d / (2n + 1)
3. n(n + 1)d / (2n)
4. n(n − 1)d / (2n + 1)

Correct answer: n(n + 1)d / (2n + 1)

Solution

The average absolute deviation from the mean in an arithmetic progression can be found by considering the symmetrical nature of the progression around its mean, leading to the formula n(n + 1)d / (2n + 1) as the correct representation of this average deviation.

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