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A quadratic pattern is given by $T_n=n^2+b_n+c$. Find the values of $b$ and $c$ if the sequence starts with the following terms: $−1;2;7;14;…$
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Sequence terms: −1;2;7;14;…

1st difference = 3; 5; 7; ...

2nd difference= 2; 2; ...

2a = 2

a = 1

3a+b = 5

b = 5 - 3(1) = 2

a+b+c = -1

c = -1 - 2 -1

c = -4

Therefore  b = 2 and c = -4
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