Question 584796: find the recursive formula of 1,5,12,22,...
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 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
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