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: Determine the common ratio r. For a geometric sequence, the term U_n can be expressed as U_n = U_p · r^n-p. Given U_3 = 2 and U_6 = (1)/(4), we can write: U_6 = U_3 · r^6-3 (1)/(4) = 2 · r^3 Divide both sides by 2: r^3 = (1)/(4 × 2) r^3 = (1)/(8) Take the cube root of both sides: r = 3/(8) r = (1)/(2) Step 2: Determine the first term U_0. We use the formula U_n = U_0 · r^n. Using U_3 = 2 and r = (1)/(2): U_3 = U_0 · r^3 2 = U_0 · ((1)/(2))^3 2 = U_0 · (1)/(8) Multiply both sides by 8: U_0 = 2 × 8 U_0 = 16 The common ratio is r = (1)/(2) and the first term is U_0 = 16. Send me the next one 📸