A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression.
Let $S_n$ represent the sum of the first $n$ terms of the harmonic progression; for example $S_3$ represents the sum of the first three terms.  If the first three terms of a harmonic progression are $3,4,6$, then:
$ \textbf{(A)}\ S_4=20 \qquad\textbf{(B)}\ S_4=25\qquad\textbf{(C)}\ S_5=49\qquad\textbf{(D)}\ S_6=49\qquad\textbf{(E)}\ S_2=\frac12 S_4 $
1. **Identify the given terms and their reciprocals:**
   The first three terms of the harmonic progression are \(3, 4, 6\). Their reciprocals are:
   \[
   \frac{1}{3}, \frac{1}{4}, \frac{1}{6}
   \]

2. **Verify that the reciprocals form an arithmetic progression:**
   Calculate the differences between consecutive terms of the reciprocals:
   \[
   \frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}
   \]
   \[
   \frac{1}{4} - \frac{1}{6} = \frac{6 - 4}{24} = \frac{1}{12}
   \]
   Since the differences are equal, the reciprocals form an arithmetic progression with a common difference of \(\frac{1}{12}\).

3. **Find the fourth term of the harmonic progression:**
   The next term in the sequence of reciprocals is:
   \[
   \frac{1}{6} - \frac{1}{12} = \frac{2 - 1}{12} = \frac{1}{12}
   \]
   The reciprocal of \(\frac{1}{12}\) is 12. Therefore, the fourth term of the harmonic progression is 12.

4. **Calculate \(S_4\), the sum of the first four terms:**
   \[
   S_4 = 3 + 4 + 6 + 12
   \]
   \[
   S_4 = 25
   \]

5. **Verify the answer choices:**
   The correct answer is \(\boxed{25}\), which corresponds to \(\textbf{(B)}\ S_4=25\).