SOLUTION: how can i find the maximum partial sum of a decreasing arithmetic sequence?

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Question 1000972: how can i find the maximum partial sum of a decreasing arithmetic sequence?
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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- Write the formula for the sum of an arithmetic progression;

- substitute numerical values of  a%5B1%5D  and  d,  the common difference;
- replace  n, the number of the terms,  by  x;

- you will get the quadratic parabola function of  x;

- find  x0  where the maximum of this quadratic function is achieved  (x-coordinate of the vertex);

- take  n  closest to  x0.