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

Form is valid through May 2019


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.


Thank you, Serge Hazanov