Final answer:
To find the nth term of the sequence, observe the differences between consecutive terms. The differences form an arithmetic sequence, suggesting the original sequence follows a quadratic pattern. Use the formula for the nth term of a quadratic sequence to determine the equation.
Step-by-step explanation:
The sequence you have provided is 3, 8, 15, 24, 35. To find the nth term of the sequence, we need to look for a pattern and determine the relationship between the terms.
If we observe the differences between consecutive terms, we can see that they form an arithmetic sequence:
5, 7, 9, 11
So, the sequence of differences is increasing by 2 each time. This suggests that the original sequence itself follows a quadratic pattern.
To find the nth term, we can use the formula for the nth term of a quadratic sequence: an = an2 + bn + c, where a, b, and c are constants.
By substituting the first few terms of the sequence into the formula, we can solve for a, b, and c to determine the equation of the quadratic sequence.