Maximum Terms satisfying a special property

The maximum number of terms is given by the formula $m+n-gcd(m,n)-1$

Here, let $m=11$ and $n=7$ and $gcd(7,11)=1$

So, putting this information in the formula above, we get the answer as $\huge{16}$ .

$\boxed{16}$ elements:

$5, 5, -13, 5, 5, 5, -13, 5, 5, -13, 5, 5, 5, -13, 5, 5$

for $17$ elements we review table

$a_1, a_2, ...., a_{11}$

$a_2, a_3, ...., a_{12}$

....................................

$a_7, a_8, ...., a_{17}$

each row is positive and each column is negative so we cannot define total sum