SOLUTION: 22,59,120,_,358. What is the missing number in the blank and how do we create a c++ program for this problem using virtual function??

Algebra ->  Sequences-and-series -> SOLUTION: 22,59,120,_,358. What is the missing number in the blank and how do we create a c++ program for this problem using virtual function??      Log On


   

Question 852459: 22,59,120,_,358.
What is the missing number in the blank and how do we create a c++ program for this problem using virtual function??
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Since we have 4 terms, we will assume a third degree 
polynomial for the nth term, because a third degree polynomial
has four coefficients.

That is, we assume a virtual function of the form

Y = A*N^3+B*N^2+C*N+D

Substitute these for (N,Y) (1,22), (2,59), (3,120), and (5,358)

    A*1^3+B*1^2+C*1+D = 22
    A*2^3+B*2^2+C*2+D = 22
    A*3^3+B*3^2+C*3+D = 22
    A*5^3+B*5^2+C*5+D = 358

And solve the augmented matrix:



We solve that matrix and get 

A = 1.83333333
B = 1
C = 21.16666667
D = -2

Then we substitute X=4 in

Y = A*N^3+B*N^2+C*N+D

and get 216.

Edwin