Question

Consider the sequence 2, 5, 10, 17, ...

Answer 1

The sequence 2, 5, 10, 17... has the pattern
1 + 1 = 2
4 + 1 = 5 
9 + 1 = 10
16 + 1  = 17
So, the next term would be:
25 + 1 = 26

The sequence is described the equation:
an = n² + 1

To solve for the nth term, the value n just has to be substituted.