Final answer:
The common difference between the numbers 6, 12, and 20 is 6. The explicit formula for this sequence is n² + 5n + 1.
Step-by-step explanation:
The common difference between the numbers 6, 12, and 20 is 6. This can be determined by subtracting each consecutive term from the previous term. For example, 12 - 6 = 6, and 20 - 12 = 8. However, if we look at the differences between the terms, we can see that the pattern is not constant. The first difference is 6, and the second difference is 8. This indicates that the sequence is quadratic rather than arithmetic. The explicit formula for this sequence is n² + 5n + 1, where n represents the position of the term in the sequence. Plugging in n = 1, 2, 3 into the formula will give you the corresponding terms of the sequence.