1. **State the problem:** Find the sum of the first 10 terms of the sequence where each term is $\frac{3}{2}$. 2. **Identify the type of sequence:** Since every term is the same ($\frac{3}{2}$), this is a constant sequence, which is a special case of an arithmetic sequence with common difference $d=0$. 3. **Formula for the sum of the first $n$ terms of an arithmetic sequence:** $$S_n = \frac{n}{2} (a_1 + a_n)$$ Since all terms are equal, $a_1 = a_n = \frac{3}{2}$. 4. **Calculate the sum:** $$S_{10} = \frac{10}{2} \left(\frac{3}{2} + \frac{3}{2}\right) = 5 \times 3 = 15$$ 5. **Explanation:** Multiplying the number of terms by the constant term gives the sum directly: $10 \times \frac{3}{2} = 15$. **Final answer:** $15$