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) About Me  (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, a%281%29%5E2%2Bb%281%29+=+1
n=2, then term #2 = 6, that is, a%282%29%5E2%2Bb%282%29+=+6
n=3, then term #3 = 15, that is, a%283%29%5E2%2Bb%283%29+=+15
n=4, then term #4 = 28, that is, a%284%29%5E2%2Bb%284%29+=+28
n=5, then term #5 = 45, that is, a%285%29%5E2%2Bb%285%29+=+45

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

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:

system%28a%281%29%5E2%2Bb%281%29+=+1%2Ca%282%29%5E2%2Bb%282%29+=+6%29 

simplifying:

system%28a%2Bb=1%2C4a%2B2b=6%29

Solve this system of equations and get a=2 and b=-1

So the ordered pair  

Edwin