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 first and second differences for the quadratic pattern. The given quadratic pattern is 19; 8; -1; -8; First differences: D_1 = 8 - 19 = -11 D_2 = -1 - 8 = -9 D_3 = -8 - (-1) = -7 Second differences: S_1 = -9 - (-11) = 2 S_2 = -7 - (-9) = 2 The second difference is constant and equal to 2. 2.1.1 Determine the next term of the pattern. The next first difference, D_4, is D_3 + 2 = -7 + 2 = -5. The next term, T_5, is T_4 + D_4 = -8 + (-5) = -13. The next term is -13. 2.1.2 Determine the general term of the quadratic number pattern. The general term for a quadratic pattern is T_n = an^2 + bn + c. Using the relationships: 2a = second difference 2a = 2 a = 1. 3a + b = first term of first differences 3(1) + b = -11 3 + b = -11 b = -14. $a + b + c = first term of