Looking at the sequence: 2, 15, 41, 80, 132, ?
Find the differences between consecutive terms:
15−2=13
41−15=26
80−41=39
132−80=52
The first differences are: 13, 26, 39, 52
Find the differences between the first differences:
26−13=13
39−26=13
52−39=13
The second differences are constant at 13, indicating a quadratic pattern.
The next first difference continues the pattern:
52+13=65
Therefore, the next term in the sequence:
132+65=197
The missing number is 197.