Final answer:
To find the nth term of the quadratic sequence, use the formula n^2 + 3n + 7.
Step-by-step explanation:
To find the nth term of the quadratic sequence, we need to observe the pattern and identify the rule. In this case, if we look at the differences between consecutive terms, we can see that they increase by 4 each time. This indicates that the sequence is quadratic. Using this information, we can write an equation to find the nth term. Let's start by writing the first few terms:
1st term: 11
2nd term: 15
3rd term: 21
4th term: 29
5th term: 39
We will use the formula n^2 + a*n + b, where a and b are constants to be determined. Plugging in the values for the first term and the second term, we get the following equations:
11 = 1^2 + a*1 + b
15 = 2^2 + a*2 + b
Simplifying these equations, we get:
a + b = 10
4a + b = 11
Solving this system of equations, we find that a = 3 and b = 7. Therefore, the nth term of the quadratic sequence is given by n^2 + 3n + 7.