Explanation
To determine the 11th term of the sequence \( m-2n, m-n, m, \ldots \), follow these steps:
1. Identify the first term (\(a\)) and the common difference (\(d\)) of the sequence:
- First term \(a = m - 2n\)
- Second term \( = m - n\)
Calculate the common difference \(d\):
\[
d = (m - n) - (m - 2n) = m - n - m + 2n = n
\]
2. Use the formula for the \(n\)-th term of an arithmetic sequence:
\[
a_n = a + (n - 1)d
\]
Here, \(n = 11\), \(a = m - 2n\), and \(d = n\).
3. Substitute these values into the formula:
\[
a_{11} = (m - 2n) + (11 - 1) \times n
\]
\[
a_{11} = (m - 2n) + 10n
\]
\[
a_{11} = m - 2n + 10n
\]
\[
a_{11} = m + 8n
\]
Thus, the 11th term of the sequence is:
D. m + 8n