Question 584796
1st difference ___ 4, 7, 10


2nd difference ___ 3, 3 ___ so formula is 2nd order (squared)


an^2 + bn + c = Tn


a(1^2) + b(1) + c = 1 ___ a + b + c = 1 ... (X)


a(2^2) + b(2) + c = 5 ___ 4a + 2b + c = 5 ... (Y)


a(3^2) + b(3) + c = 12 ___ 9a + 3b + c = 12 ... (Z)


subtracting X from Y ___ 3a + b = 4 ... (V)


subtracting X from z ___ 8a + 2b = 11 ... (W)


subtracting 2V from W ___ 2a = 3 ___ a = 3/2


b = -1/2 ___ c = 0


Tn = (3n^2 - n) / 2