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
Here's how to find the value of u_4: The sequence is defined by the recurrence relation U_n+2 = 5U_n+1 - 6U_n for n ≥ 1. We are given u_1 = 1 and u_2 = 2. Step 1: Calculate u_3. Set n=1 in the recurrence relation: U_1+2 = 5U_1+1 - 6U_1 U_3 = 5U_2 - 6U_1 Substitute the given values u_1 = 1 and u_2 = 2: U_3 = 5(2) - 6(1) U_3 = 10 - 6 U_3 = 4 Step 2: Calculate u_4. Set n=2 in the recurrence relation: U_2+2 = 5U_2+1 - 6U_2 U_4 = 5U_3 - 6U_2 Substitute the calculated value u_3 = 4 and the given value u_2 = 2: U_4 = 5(4) - 6(2) U_4 = 20 - 12 U_4 = 8 The value of u_4 is 8. That's 2 down. 3 left today — send the next one.