Here is our new Problem:
In an arithmetic sequence, u7+u8+u9 > 0 and u7+u10 < 0.
For what value of n, Sn is maximum ?
Answer Submission Is Not Available
Dear friends and visitors of the site.
The problem was quite popular, we received a lot of answers.
The first correct solution was delivered by Jane.
Our congratulations to her!Here is my solution:
u7+u9=2*u8 (arithmetic sequence). Hence u8 >0.
u7+u10=u8+u9 (property of an arithmetic sequence).
Thus u8+u9<0, so u9 is the first negative term.
Thus S8 is the maximal value of the sum.
n=8.Thank you, Serge Hazanov