https://file.aiquickdraw.com/mathbot/file/17262271130307eo9ofyb.jpg

The given image contains the following mathematical information:

- \( X_1 = 2 \), \( X_2 = 4 \), \( X_3 = 5 \), \( X_4 = 10 \)
- A summation expression is provided as:
  \[
  \sum_{n=1}^{4} (3X_n + 1)
  \]

### Solving the summation step-by-step:

We need to calculate the sum:
\[
\sum_{n=1}^{4} (3X_n + 1)
\]
This means we substitute the values of \( X_n \) from \( n=1 \) to \( n=4 \) and sum up the results.

1. For \( n=1 \), \( X_1 = 2 \):
   \[
   3X_1 + 1 = 3(2) + 1 = 6 + 1 = 7
   \]
2. For \( n=2 \), \( X_2 = 4 \):
   \[
   3X_2 + 1 = 3(4) + 1 = 12 + 1 = 13
   \]
3. For \( n=3 \), \( X_3 = 5 \):
   \[
   3X_3 + 1 = 3(5) + 1 = 15 + 1 = 16
   \]
4. For \( n=4 \), \( X_4 = 10 \):
   \[
   3X_4 + 1 = 3(10) + 1 = 30 + 1 = 31
   \]

Now, summing these values:
\[
7 + 13 + 16 + 31 = 67
\]

Thus, the value of the summation is **67**.

Let me know if you want any more details or explanations.

### Follow-up questions:
1. How does changing \( X_n \) affect the summation?
2. What happens if the summation limit changes to \( n = 5 \)?
3. Can we simplify the expression further by factoring out constants?
4. How would the result change if the function inside the summation were \( 2X_n + 3 \) instead?
5. How can we generalize this summation formula for an arbitrary number of terms?

**Tip**: When dealing with summations, ensure to properly substitute values and always check each term for correctness before summing.

Evaluate the summation \( \sum_{n=1}^{4} (3X_n + 1) \) where \( X_1 = 2 \), \( X_2 = 4 \), \( X_3 = 5 \), and \( X_4 = 10 \).

Learn how to solve a summation problem with a step-by-step guide. Given values \( X_1 = 2 \), \( X_2 = 4 \), \( X_3 = 5 \), and \( X_4 = 10 \), we substitute and evaluate the expression \( \sum_{n=1}^{4} (3X_n + 1) \). Suitable for students in Grades 8-10.

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