Given a sequence of numbers: 2, 5, 10, 17, find the formula for the nth term and calculate the 8th term of the sequence.

Step 1 ：The given sequence is 2, 5, 10, 17. We can notice that the difference between the consecutive terms is increasing by 2 each time. So the sequence can be a quadratic sequence, and the general formula for a quadratic sequence is \(an^{2} + bn + c\).

Step 2 ：To find the values of a, b, and c, we can set up a system of equations using the first three terms of the sequence: \[\begin{cases}a + b + c = 2\\4a + 2b + c = 5\\9a + 3b + c = 10\end{cases}\]

Step 3 ：Solving the system of equations, we get \(a = 1\), \(b = 1\), and \(c = 0\). So the nth term of the sequence is \(n^{2} + n\).

Step 4 ：Substitute n = 8 into the formula \(n^{2} + n\), we get the 8th term of the sequence.