To find the sum of the sequence \(23 + 25 + 27 + \ldots + 135 + 137\), we first recognize that this is an arithmetic sequence.

An arithmetic sequence has the form:
\[ a, a + d, a + 2d, \ldots, a + (n-1)d \]

where:
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the number of terms.

For this sequence:
- The first term \( a = 23 \),
- The common difference \( d = 2 \).

We need to find the number of terms \( n \) in the sequence. The last term \( l \) is 137.

The \( n \)-th term of an arithmetic sequence is given by:
\[ a + (n-1)d = l \]

Plugging in the known values:
\[ 23 + (n-1) \cdot 2 = 137 \]

Solving for \( n \):
\[ 23 + 2n - 2 = 137 \]
\[ 2n + 21 = 137 \]
\[ 2n = 116 \]
\[ n = 58 \]

So, there are 58 terms in the sequence.

The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence is given by:
\[ S_n = \frac{n}{2} \cdot (a + l) \]

Plugging in the values:
\[ S_{58} = \frac{58}{2} \cdot (23 + 137) \]
\[ S_{58} = 29 \cdot 160 \]
\[ S_{58} = 4640 \]

Therefore, the sum of the sequence \( 23 + 25 + 27 + \ldots + 135 + 137 \) is \( 4640 \).