This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate U_3. We use the formula U_n = 2 ((2)/(3))^n. Substitute n=3: U_3 = 2 ((2)/(3))^3 = 2 × (2^3)/(3^3) = 2 × (8)/(27) = (16)/(27) Step 2: Calculate U_0. We use the formula U_n = 2 ((2)/(3))^n. Substitute n=0: U_0 = 2 ((2)/(3))^0 = 2 × 1 = 2 Step 3: Calculate V_6. First, we find U_6: U_6 = 2 ((2)/(3))^6 = 2 × (2^6)/(3^6) = 2 × (64)/(729) = (128)/(729) Now, we use the formula V_n = (U_n): V_6 = (U_6) = ((128)/(729)) Using logarithm properties, ((a)/(b)) = (a) - (b) and (a^b) = b (a): V_6 = (2^7) - (3^6) = 7 (2) - 6 (3) The calculated values are: U_3 = (16)/(27) U_0 = 2 V_6 = 7 (2) - 6 (3) Send me the next one 📸