How Do You Solve a System with Infinitely Many Solutions?

[EV33]

1. Homework Statement

The following system of linear equations has infinitely many solutions.
{xi + xi+1 + xi+2 = 0 : 1 < i < 7}

3. The Attempt at a Solution
I feel like I have the capacity to solve this problem however I can't interpret what the question is even asking with all the i's in it.
If someone could just interpret the question for me that would be very helpful.

 

[HallsofIvy]

1. Homework Statement

The following system of linear equations has infinitely many solutions.
{xi + xi+1 + xi+2 = 0 : 1 < i < 7}

3. The Attempt at a Solution
I feel like I have the capacity to solve this problem however I can't interpret what the question is even asking with all the i's in it.
If someone could just interpret the question for me that would be very helpful.

Be careful with your notation. I would interpret x_(i+1) as $x_{i+1}$ but I would interpret xi+1 as $x_i+ 1$. That confused me for a moment!

If your problem is $\{x_i+ x_{i+1}+ x_{i+2}= 0: 1< i< 7\}$, then you have 7 equations in 9 unknown values.

$x_1+ x_2+ x_3= 0$
$x_2+ x_3+ x_4= 0$
$x_3+ x_4+ x_5= 0$
$x_4+ x_5+ x_6= 0$
$x_5+ x_6+ x_7= 0$
$x_6+ x_7+ x_8= 0$
$x_7+ x_8+ x_9= 0$