Question

What is the nth term in the sequence: 4, 7, 12, 19, 28 Please show working out

Answer 1

                         4, 7, 12, 19, 28
1st difference    +3 +5 +7 +9
2nd difference      +2 +2  +2

This is a geometric sequence

The form is:
                  an² + bn + c
2a is always = to the second difference
2a = 2
a = 1

3a + b = 2nd term - 1st term
3(1) + b = 3
3 + b = 3
b = 0

a + b + c = 1st term
1 + 0 + c = 4
1 +c = 4
c = 3

nth term of sequence {substitute all we have found}
1n² + 0 + 3
n² + 3