1. We are given a harmonic sequence where the 2nd term is $\frac{1}{2}$ and the 6th term is $\frac{1}{6}$. We need to find the 5th term. 2. Recall that a harmonic sequence is the sequence whose terms are the reciprocals of an arithmetic sequence. Let the arithmetic sequence be $a_n$. Then, $\frac{1}{a_2} = \frac{1}{2}$ and $\frac{1}{a_6} = \frac{1}{6}$. 3. From these, $a_2 = 2$ and $a_6 = 6$. 4. Since $a_n$ is arithmetic, we can write: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 5. Using $a_2 = 2$: $$a_1 + d = 2$$ Using $a_6 = 6$: $$a_1 + 5d = 6$$ 6. Subtract the first equation from the second: $$a_1 + 5d - (a_1 + d) = 6 - 2$$ $$4d = 4$$ $$d = 1$$ 7. Substitute $d=1$ back into $a_1 + d = 2$: $$a_1 + 1 = 2$$ $$a_1 = 1$$ 8. Now find the 5th term of the arithmetic sequence $a_5$: $$a_5 = a_1 + 4d = 1 + 4 \times 1 = 5$$ 9. The 5th term of the harmonic sequence is the reciprocal of $a_5$: $$\boxed{\frac{1}{5}}$$