1. **State the problem:** We want to analyze the sequence defined by $a_n = 3n \times \left(\frac{1}{3}\right)^n$. 2. **Formula and explanation:** The sequence is given by multiplying the term number $n$ by $3$ and then by $\left(\frac{1}{3}\right)^n$. This is a geometric term multiplied by a linear term. 3. **Simplify the expression:** $$a_n = 3n \times \left(\frac{1}{3}\right)^n = 3n \times 3^{-n} = 3n \times 3^{-n} = n \times 3^{1-n}$$ 4. **Interpretation:** As $n$ increases, $3^{1-n}$ decreases exponentially because the exponent $1-n$ becomes more negative, while $n$ increases linearly. 5. **Behavior:** The sequence terms get smaller as $n$ grows large because the exponential decay dominates the linear growth. **Final simplified form:** $$a_n = n \times 3^{1-n}$$