The summation given is:

$\sum_{i=1}^n x_i$

where $x_1 = 5$, $x_2 = 15$, $x_3 = 3$, $x_4 = 3$, $x_5 = 8$, $x_6 = 10$, and $x_7 = 12$. To find the value of this summation from $i=1$ to $n=7$, we add up all these values:

$5 + 15 + 3 + 3 + 8 + 10 + 12 = 56$

So,

$\sum_{i=1}^7 x_i = 56$

The answer is 56.

Would you like more details on the steps?

Here are some related questions for further exploration:

1. How does changing the upper limit in a summation affect the total?
2. How can we represent this summation if we add another term, say $x_8$?
3. What happens to the summation if one of the $x_i$ values changes?
4. How can we use summations to express the mean of the values?
5. What are common notations and properties for summations in algebra?

Tip: Summations are a quick way to add series of values, and they often simplify expressions in algebra, calculus, and statistics!