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.