Solution:

Given, the numbers are 1, 1+d, 1+2d, ..., 1+8d.

Let's find the mean of these numbers.

Mean = (1 + 1+d + 1+2d + ... + 1+8d) / 9

= (9/2) + 4d

Now, let's find the deviation of each number from the mean.

Deviation of 1 from mean = (1 - [(9/2) + 4d]) = (-5/2 - 4d)

Deviation of 1+d from mean = (1+d - [(9/2) + 4d]) = (-3/2 - 3d)

Similarly, we can find deviations of all other numbers from the mean.

Now, let's find the mean deviation.

Mean deviation = (|(-5/2 - 4d)| + |(-3/2 - 3d)| + ... + |(7/2 - 4d)|) / 9

= (|(-5 - 8d/2)| + |(-3 - 6d/2)| + ... + |(7 - 8d/2)|) / 9

= (|(-5 - 4d)| + |(-3 - 3d)| + ... + |(7 - 4d)|) / 9

= ((5 + 4d) + (3 + 3d) + ... + (7 - 4d)) / 9

= (32 + 9d) / 9

Given, mean deviation = 205

So, (32 + 9d) / 9 = 205

32 + 9d = 1845

9d = 1813

d = 1813/9

d = 201.44

Since, d should be an integer, the closest integer to 201.44 is 201.

But, the correct answer is 10.

So, we made some mistake in our calculations. Let's check.

Mean deviation = (|(-5 - 4d)| + |(-3 - 3d)| + ... + |(7 - 4d)|) / 9

= ((5 + 4d) + (3 + 3d) + ... + (7 - 4d)) / 9

= (|(-5 - 4d)| + |(-3 - 3d)| + ... + |(7 - 4d)| + |(9 - 4d)|) / 9 - |(9 - 4d)|/9

= ((5 + 4d) + (3 + 3d) + ... + (7 - 4d) + (9 - 4d)) / 9 - |(9 - 4d)|/9

= (36 + 9d) / 9 - |(9 - 4d)|/9

= (4 + d) - |(9 - 4d)|/9

Given, mean deviation = 205

So, (4 + d) - |(9 - 4d)|/9 = 205

4 + d - |(9 - 4d)|/