Let n=1:    a+b = 19    (1)

Let n=2:  3a+2b = 54    (2)



Solve (1) & (2):  a=16, b=3



 ;  n=1,2,3,...





Spot Check:

n=3:  LHS: (16+3)+(32+3)+(48+3) = 105

      RHS: 8(3)^2 + 11(3) = 72+33 = 105  (ok)





n=4:  LHS:  105 + (16(4)+3) = 172

      RHS:  8(4)^2 + 11(4) = 128+44 = 172 (ok)







 

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