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

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Question 842180: how many terms in the series 19+16+13...must be added to give a sum of 44
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The first term of the SEQUENCE is 19.
The difference between terms is NEGATIVE 3.
The n term of the SEQUENCE is 19%2B%28n-1%29%2A%28-3%29.

The formula for Arithmetic SERIES is %28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29.
You want this equation: highlight_green%28%28n%2F2%29%2819%2B19%2B%28n-1%29%2A%28-3%29%29=44%29.

SOLUTION STEPS
%28n%2F2%29%2838%2B%28-3n%2B3%29%29=44
n%2841-3n%29=88
41n-3n%5E2=88
3n%5E2-41n%2B88=0
Discriminant+=+625 and sqrt%28625%29=25; this is done for using general solution to a quadratic equation and avoid trying to factor the quadratic expression.
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n=%2841%2B-+25%29%2F%286%29 without showing all the steps for this formula.
The MINUS form will give a bad value, a mixed number while the PLUS form gives highlight%28highlight%28n=11%29%29.

What you might try, to be sure, find the sum of this:
19%2B16%2B13%2B10%2B7%2B4%2B1%2B%28-2%29%2B%28-5%29%2B%28-8%29%2B%28-11%29