SOLUTION: How many terms in the series 19+16+13+... Must be added to a sum of 44?

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Question 1018377: How many terms in the series 19+16+13+... Must be added to a sum of 44?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Sn = n%2F2[2a1 + (n-1)d]

44 = n%2F2[2(19) + (n-1)(-3)]

44 = n%2F2[38 -3n + 3]

44 = n%2F2[41 - 3n]

88 = n[41 - 3n]

88 = 41n - 3n2

3n2 - 41n + 88 = 0

(3n-8)(n-11) = 0

3n-8 = 0;  n-11 = 0
  3n = 8;     n = 11
   n = 8/3

The answer n has to be a positive integer,

so the answer is 11 terms.

Checking: 19+16+13+10+7+4+1-2-5-8-11 = 44
 
Edwin