SOLUTION: Determine the x value on this sequence (16,35,x,91) and T1,T5and T2 are not given

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Question 947874: Determine the x value on this sequence (16,35,x,91) and T1,T5and
T2 are not given
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
y,z,16,35,x,91

Assume the general term is quadratic: 

 <--general term

Substituting n=3, T3=16





Substituting n=4, T2=35





Substituting n=6, T6=91





We have the system of equations:



Solve that system of equation and get

A=3, B=-2, C=-5

Substitute into our assumed general term:




. Substituting n=5






. Substituting n=1






. Substituting n=1







The sequence is -4,3,16,35,60,91,128,171,220,275,336,403,...

Edwin
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