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**Problem Summary:**

Pablo is walking up a building with 5 floors, where the number of apartments on each floor corresponds to the values of \( 2x + 1 \), where \( x = 1, 2, 3, 4, 5 \) respectively.

Additionally, we are given a set \( S = \{2, 5, 8, 11, 14\} \) and a set \( T \) which consists of the values \( 2x - 1 \) for \( x = 1, 2, 3, 4, 5 \).

Finally, the problem asks us to find the total number of apartments in the building that Pablo counts.

**Step-by-Step Solution:**

1. **Expression for apartments on each floor:**

   The number of apartments on each floor is given by the expression \( 2x + 1 \) where \( x \) takes values from 1 to 5.

   - For \( x = 1 \): Number of apartments = \( 2(1) + 1 = 3 \)
   - For \( x = 2 \): Number of apartments = \( 2(2) + 1 = 5 \)
   - For \( x = 3 \): Number of apartments = \( 2(3) + 1 = 7 \)
   - For \( x = 4 \): Number of apartments = \( 2(4) + 1 = 9 \)
   - For \( x = 5 \): Number of apartments = \( 2(5) + 1 = 11 \)

   So, the total number of apartments Pablo sees on the 5 floors is:
   \[
   3 + 5 + 7 + 9 + 11 = 35
   \]

2. **Set \( T \):**

   The set \( T \) is generated by the formula \( 2x - 1 \) for \( x = 1, 2, 3, 4, 5 \). We can compute the elements as follows:

   - For \( x = 1 \): \( 2(1) - 1 = 1 \)
   - For \( x = 2 \): \( 2(2) - 1 = 3 \)
   - For \( x = 3 \): \( 2(3) - 1 = 5 \)
   - For \( x = 4 \): \( 2(4) - 1 = 7 \)
   - For \( x = 5 \): \( 2(5) - 1 = 9 \)

   Therefore

Pablo es propietario de un edificio con 5 pisos, donde el número de departamentos en cada piso sigue la fórmula 2x + 1, con x = 1, 2, 3, 4, 5. Se pide determinar el número total de departamentos en el edificio.

This problem involves calculating the total number of apartments in a building using the arithmetic sequence 2x + 1 for different values of x. Suitable for students in Grades 9-12.

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