Final answer:
To find the nth term of the given sequence, we can use the quadratic formula to identify the pattern and obtain the general formula.
Step-by-step explanation:
The given sequence is: 3, 20, 47, 84
To find the nth term, we need to find the pattern in the sequence. Looking at the differences between consecutive terms, we can observe that the differences are increasing by 17, 27, and 37 respectively. This suggests that the pattern for the differences is quadratic.
Using the quadratic formula, we can find the general formula for the nth term of the sequence, which is:
An = (n2 - 5n + 6)