The first two terms of an arithmetic sequence are \( m \) and \( n \), respectively. Calculate the 10th term.

In an arithmetic sequence, each term is generated by adding a constant difference, known as the common difference, to the previous term. Given the first two terms \( m \) and \( n \), we can determine the common difference \( d \) as follows: \[ d = n - m \] The \( k \)-th term of an arithmetic sequence can be expressed as: \[ a_k = a_1 + (k-1)d \] where \( a_1 \) is the first term. In this case, the first term \( a_1 \) is \( m \) and we want to find the 10th term \( a_{10} \): \[ a_{10} = m + (10-1)(n - m) \] Simplifying this gives: \[ a_{10} = m + 9(n - m) \] \[ a_{10} = m + 9n - 9m \] \[ a_{10} = 9n - 8m \] So, the 10th term of the sequence is \( 9n - 8m \).