Final answer:
The student's question about a number sequence 101, 104, 109 is resolved by identifying the correct expression that represents this sequence. Upon testing the given options, option B: n² + n + 100 correctly matches the sequence, making it the answer.
Step-by-step explanation:
The student is asking for help to determine the correct expression that represents a particular number sequence. The sequence provided is 101, 104, 109, which suggests that the next terms increase by a value that is more than the constant difference found in arithmetic sequences, indicating a possible quadratic relationship. We can use the initial terms of the sequence to test each option provided by the student.
To find out which expression correctly represents the sequence, we need to plug in values for n and see if the expression's output matches the sequence given. Let's consider n = 1 for the first term, n = 2 for the second term, and so on. Testing the provided options A, B, C, and D:
- Option A: 2n + 99
- Option B: n² + n + 100
- Option C: 2n + 100
- Option D: n² + n + 99
We find that option B matches the sequence when n=1, 2, and 3. Therefore, the correct option to represent the sequence 101, 104, 109, ... is B: n² + n + 100.