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Thursday, 11 June 2026
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What is the 11th term of the sequence: m-2n, m-n, m...?

What is the 11th term of the sequence: m-2n, m-n, m...?
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  • A M+n
  • B M-n
  • C M + 6n
  • D M+ 8n
Correct Answer: Option D
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

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