Question

find the nth term of the sequence

Answer 1

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