Let the first term be \(a\) and the common difference be \(d\).

The sixth term is given by \(a + 5d = 23\).

The sum of the first ten terms is given by \(\frac{10}{2} (2a + 9d) = 200\), simplifying to \(5(2a + 9d) = 200\).

Solving the equations:

1. \(a + 5d = 23\)

2. \(5(2a + 9d) = 200\) simplifies to \(2a + 9d = 40\).

From equation 1, \(a = 23 - 5d\).

Substitute \(a = 23 - 5d\) into equation 2:

\(2(23 - 5d) + 9d = 40\)

\(46 - 10d + 9d = 40\)

\(46 - d = 40\)

\(d = 6\)

Substitute \(d = 6\) back into \(a = 23 - 5d\):

\(a = 23 - 5(6)\)

\(a = 23 - 30\)

\(a = -7\)

The seventh term is \(a + 6d = -7 + 6(6) = -7 + 36 = 29\).