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

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Question 1071573: How many terms in the series 19+16+13 must be added to give a sum of 44?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


19+16+13+...+? = 44

matrix%281%2C3%2C+++++++a%5B1%5D=19%2C%22%2C%22%2Cd=-3%29







matrix%281%2C3%2C%0D%0A%0D%0A44%2C%22%22=%22%22%2Cexpr%28n%2F2%29%2838-3n%2B3%29%29

matrix%281%2C3%2C%0D%0A%0D%0A44%2C%22%22=%22%22%2Cexpr%28n%2F2%29%2841-3n%29%29

matrix%281%2C3%2C%0D%0A%0D%0A88%2C%22%22=%22%22%2Cn%2841-3n%29%29

matrix%281%2C3%2C%0D%0A%0D%0A88%2C%22%22=%22%22%2C41n-3n%5E2%29

matrix%281%2C3%2C%0D%0A%0D%0A3n%5E2-41n%2B88%2C%22%22=%22%22%2C0%29

matrix%281%2C3%2C%0D%0A%0D%0A%283n-8%29%28n-11%29%2C%22%22=%22%22%2C0%29

3n-8=0  has fractional solution 8/3 which
we ignore.

n-11=0 gives the answer n = 11

Check

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

Edwin