0
t(n) = 5 6 8 11 15
First differences = 1 2 3 4
Second differences = 1 1 1
So the sequence is quadratic with the coefficient of n2 being half of the second difference ie half of 1.
So t(1) = 0.5*12 + b*1 + c = 5 ie b + c = 4.5
and
So t(2) = 0.5*22 + b*2 + c = 6 ie 2b + c = 4
Solving these two equations simultaneously, b = -0.5 and c = 5
Therefore, the sequence is t(n) = (n2 - n + 10)/2
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