To solve the problem, we need to find the values of \( Q_2 \) and \( U_2 \) from the given sequences and then calculate their product. Let's break this down step-by-step. ### Step 1: Calculate \( Q_2 \) The formula for the sequence \( Q_n \) is given as: \[ Q_n = 3 \cdot 2^{n - 2} \] To find \( Q_2 \), we substitute \( n = 2 \): \[ Q_2 = 3 \cdot 2^{2 - 2} \] Calculating the exponent: \[ Q_2 = 3 \cdot 2^{0} \] Since \( 2^0 = 1 \): \[ Q_2 = 3 \cdot 1 = 3 \] ### Step 2: Calculate \( U_2 \) The formula for the sequence \( U_m \) is given as: \[ U_m = 3 \cdot 2^{2m - 3} \] To find \( U_2 \), we substitute \( m = 2 \): \[ U_2 = 3 \cdot 2^{2 \cdot 2 - 3} \] Calculating the exponent: \[ U_2 = 3 \cdot 2^{4 - 3} = 3 \cdot 2^{1} \] Since \( 2^1 = 2 \): \[ U_2 = 3 \cdot 2 = 6 \] ### Step 3: Calculate the Product \( Q_2 \cdot U_2 \) Now that we have both \( Q_2 \) and \( U_2 \): \[ Q_2 = 3 \quad \text{and} \quad U_2 = 6 \] We can find the product: \[ Q_2 \cdot U_2 = 3 \cdot 6 = 18 \] ### Conclusion The product of \( Q_2 \) and \( U_2 \) is \( 18 \). ### Explanation of Options - **Option A: 18** - This is the correct answer as we calculated \( Q_2 \cdot U_2 = 18 \). - **Option B: 12** - This is incorrect. It may arise from a miscalculation, perhaps by incorrectly calculating \( U_2 \) or \( Q_2 \). - **Option C: 6** - This is incorrect. It could be a misunderstanding of the product of the two terms, possibly thinking only one of the terms was needed. - **Option D: 3** - This is incorrect. It seems to be the value of \( Q_2 \) alone, not the product. ### Revision Summary - The nth term of the sequences are calculated by substituting the respective values into the formulas. - For \( Q_2 \), we found \( 3 \) and for \( U_2 \), we found \( 6 \). - The product \( Q_2 \cdot U_2 \) is \( 18 \). - Always double-check calculations to avoid common pitfalls in exponentiation and multiplication.