The nth term of the quadratic sequence in the question is n² + 3
Given the sequence :
The first difference ;
- 7 - 4 ; 12 - 7; 19 - 12 ; 28 - 19 = 3, 5, 7, 9
The second difference ;
- 5 - 3 ; 7 - 5 ; 9 - 7 = 2, 2, 2
Hence, second difference = 2
Half of the second difference, a = 2/2 = 1, hence, a = 1
3a + b = second term - first term
3a + b = 7 - 4
3a + b = 3
3(1) + b = 3
3 + b = 3
b = 3 - 3
b = 0
a + b + c = First term
1 + 0 + c = 4
c + 1 = 4
c = 4 - 1
c = 3
The nth term of a quadratic sequence can be expressed as :
Tn = an² + bn + c
Tn = 1(n²) + 0(n) + 3
Therefore, the nth term of the quadratic sequence is n² + 3
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