# SOLUTION: Use the Method of Finite Differences to find a function for the following sequences. 2.5, 6, 13.5, 25

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: Use the Method of Finite Differences to find a function for the following sequences. 2.5, 6, 13.5, 25      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Sequences-and-series Question 572645: Use the Method of Finite Differences to find a function for the following sequences. 2.5, 6, 13.5, 25Answer by Edwin McCravy(8914)   (Show Source): You can put this solution on YOUR website!```n tn D1 D2 --------------- 1 2.5 3.5 4 2 6.0 7.5 4 3 13.5 11.5 4 25.0 Since it took 2 differences to get to a column that only had the same number in it, we can assume a 2nd degree polynomial function for tn of the form: tn = An² + Bn + C Substituting t1 = A(1)² + B(1) + C 2.5 = A(1) + B(1) + C 2.5 = A + B + C t2 = A(2)² + B(2) + C 6.0 = A(4) + B(2) + C 6.0 = 4A + 2B + C t3 = A(3)² + B(3) + C 13.5 = A(9) + B(3) + C 13.5 = 9A + 3B + C So we have this system 2.5 = A + B + C 6.0 = 4A + 2B + C 13.5 = 9A + 3B + C or maybe you would write it this way: A + B + C = 2.5 4A + 2B + C = 6.0 9A + 3B + C = 13.5 Solve that system of 3 equations in three unknowns and get: A = 2, B = -2.5, C = 3 So the function tn = An² + Bn + C becomes tn = 2n² - 2.5n + 3 Edwin```