## Problem

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

## Solution

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
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