SOLUTION: in the sequence 1, 6, 15, 28, 45 and so on, the nth term of the sequence is given by a quadratic polynomial, an^2+bn. what is the ordered pair (a,b)?

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Question 171676: in the sequence 1, 6, 15, 28, 45 and so on, the nth term of the sequence is given by a quadratic polynomial, an^2+bn. what is the ordered pair (a,b)?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

in the sequence 1, 6, 15, 28, 45 and so on, the nth term of the sequence is given by a quadratic polynomial, an^2+bn. what is the ordered pair (a,b)?

This means when

n=1, then term #1 = 1, that is, 
n=2, then term #2 = 6, that is, 
n=3, then term #3 = 15, that is, 
n=4, then term #4 = 28, that is, 
n=5, then term #5 = 45, that is, 

We can take any two of those equations as a system, and
solve for  and 

We might as well take the easiest two, which are the
first and second equations, although we could take
any two of them as a system:

 

simplifying:



Solve this system of equations and get  and 

So the ordered pair  

Edwin
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