The image asks to calculate the sum:

$\sum_{i=2}^{8} x_i$

The table provided contains values of $x_i$ for different values of $i$. Let's extract the relevant values from the table and calculate the sum.

For $i = 2$ to $i = 8$, the corresponding $x_i$ values are:

• $x_2 = 17$
• $x_3 = 20$
• $x_4 = 8$
• $x_5 = 7$
• $x_6 = 18$
• $x_7 = 2$
• $x_8 = 18$

Now, let's compute the sum:

$\sum_{i=2}^{8} x_i = 17 + 20 + 8 + 7 + 18 + 2 + 18$

I will calculate this sum for you.The sum $\sum_{i=2}^{8} x_i$ is $90$.

Would you like more details or have any further questions? Here are some related questions that expand on this topic:

1. How would the sum change if the range was from $i=1$ to $i=8$?
2. How can this type of summation be represented using sigma notation for different ranges?
3. What are the properties of summation that make calculations like this easier?
4. How would the result change if we had different starting or ending indices for the sum?
5. How does summation relate to integral calculus for continuous functions?

Tip: When summing values in a table, always double-check the indices and make sure you include only the specified range.