Multiple choice

The mean deviation from the mean of the A.P. $a, a+d, a+2d, ........., a+2nd$ is

  1. $n(n+1)d$
  2. $\frac{n(n+1)d}{2n+1}$
  3. $\frac{n(n+1)d}{2n}$
  4. $\frac{n(n-1)d}{2n-1}$
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B Correct answer
Explanation

The mean of the AP is a + nd. The mean deviation from the mean for an AP with 2n+1 terms is given by the formula (n(n+1)d)/(2n+1).

AI explanation

For the given arithmetic progression, calculate the mean by averaging the first and last terms: (a + a + 2nd) / 2, which simplifies to a + nd. To find the mean deviation, use the general formula for an arithmetic progression with an odd number of terms: n(n+1)d divided by (2n+1). The mean deviation from the mean is therefore n(n+1)d / (2n+1).

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