SOLUTION: Hence,Find a and b if {{{sum( ak+b, k=1, n ) = 8n^2+11n}}} for all positive integers n.

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Question 1170792: Hence,Find a and b if sum%28+ak%2Bb%2C+k=1%2C+n+%29+=+8n%5E2%2B11n for all positive integers n.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


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

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



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



+highlight%28+sum%28%2816k%2B3%29%2C+k=1%2C+n%29+=+8n%5E2%2B11n%29+ ;  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)