Question

Find the nth term of this quadratic sequence. 3, 11, 25, 45

Answer 1

Answer:

3 , 11, 25, 45

Diff 8 14 20

Diff 6 6

The second differences are the same. The sequence is quadratic and will contain an n^2 term. The coefficient of n^2 is always half of the second difference. In this example, the second difference is 6. Half of 6 is 3 so the coefficient of n^2 is 3

therefore 3n^2

3 11 25 45

3n^2 3 12 27 48

Remainder 0 -1 -2 -3

Difference -1 -1 -1

linear sequence with nth term -n+1

so nth term of quadratic sequence in 3n^2-n+1