Question 1170792
<pre>
Let n=1:    a+b = 19    (1)
Let n=2:  3a+2b = 54    (2)

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

{{{ highlight( sum((16k+3), k=1, n) = 8n^2+11n) }}} ;  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)