The problem in the image is asking for the 2021st term of a sequence made up of positive integers that are multiples of 2 or multiples of 3. These numbers include all multiples of 2, 3, 4, 6, 8, 9, 10, and 12.

Key Points:

• Multiples of 2: Include numbers like 2, 4, 6, 8, 10, 12, etc.
• Multiples of 3: Include numbers like 3, 6, 9, 12, etc.
• The sequence is a union of numbers that are divisible by either 2 or 3.

Now, I will calculate the 2021st term by determining the number of integers divisible by 2 or 3. This is similar to finding the union of multiples of 2 and 3 up to a certain value.

Let's go ahead and calculate it.

Using the inclusion-exclusion principle, I calculated that there are 1,347 numbers that are divisible by 2 or 3 up to a certain point. However, this means we need to continue looking for numbers until we reach the 2021st term of this sequence.

Let's calculate further to find the exact value corresponding to the 2021st term in the sequence that includes both multiples of 2 and 3.From the calculations, the 2021st term in the sequence that includes multiples of 2 or 3 is 3032.

Thus, the correct answer is B. 3032.

Would you like further details or explanations on this? Here are some related questions you might find helpful:

1. How is the inclusion-exclusion principle applied in this context?
2. What are the common multiples of 2 and 3, and how do they affect the sequence?
3. How can we generalize the process of finding any term in a sequence like this?
4. What role does the least common multiple (LCM) play in these types of problems?
5. How would the problem change if we included more multiples, such as those of 5 or 7?

Tip: When solving problems involving multiples, always remember to account for overlaps using the inclusion-exclusion principle.