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
Hey Ðƴŋâmïč̣, good to see you again. Here's how to find the terms of the sequence: Step 1: Calculate U_2. We use the formula U_n+1 = 3 + (1)/(4) U_n with n=1. U_2 = 3 + (1)/(4) U_1 Substitute U_1 = 5: U_2 = 3 + (1)/(4) (5) U_2 = 3 + (5)/(4) U_2 = (12)/(4) + (5)/(4) U_2 = (17)/(4) Step 2: Calculate U_3. We use the formula U_n+1 = 3 + (1)/(4) U_n with n=2. U_3 = 3 + (1)/(4) U_2 Substitute U_2 = (17)/(4): U_3 = 3 + (1)/(4) ((17)/(4)) U_3 = 3 + (17)/(16) U_3 = (48)/(16) + (17)/(16) U_3 = (65)/(16) Step 3: Calculate U_4. We use the formula U_n+1 = 3 + (1)/(4) U_n with n=3. U_4 = 3 + (1)/(4) U_3 Substitute U_3 = (65)/(16): U_4 = 3 + (1)/(4) ((65)/(16)) U_4 = 3 + (65)/(64) U_4 = (192)/(64) + (65)/(64) U_4 = (257)/(64) The terms are: U_2 = (17)/(4) U_3 = (65)/(16) U_4 = (257)/(64) Send me the next one 📸