Question

Find the nth term of the following sequence:

5, 20, 45, 80, 125

Answer 1

So, 5, 20, 45, 80,...5N2

Explanation:

Divide the sequence by 5 and the answer becomes very obvious:

EX: 1, 4, 9, 16,...N2

Answer 2

quadratic sequence formula : an^2+bn+c

2nd difference 2a = 10
a = 5

1st difference 3a+b = 15
substitute 5 into a
3(5)+b = 15
b = 0

nth term rule : a + b + c = 5
substitute a and b values into equation
5 + 0 + c = 5
c = 0

nth term : 5n^2