This is a Changing Difference Sequences:
Given: 11 20 35 56 83
1st difference : 9 15 21 27
2nd difference: 6 6 6
Formula : nth term = a + (n - 1)d + ½(n - 1)(n - 2)c
a = first term = 11
c = second difference = 6
d = difference between the first and the term
So we substitute all these known values into the formula:
nth term = 11 + (n - 1)(9) + 1/2(n - 1)(n - 2)(6)
nth term = 11 + 9n - 9 + 3(n - 1)(n - 2)
nth term = 11 + 9n - 9 + 3(n² - 3n + 2)
nth term = 11 + 9n - 9 +3n² - 9n + 6
nth term = 3n² + 8
Answer: 3n² + 8
