Question

The nth term of a quadratic sequence is an^2 + bn + c.

Here are its first four terms.
4 12 26 46
Find the values of a, b and c.

Answer 1

a = 3, b = -1, c = 2

Explanation:

an^2 + bn + c

n = 1:

a + b + c = 4 Eq. 1

n = 2:

4a + 2b + c = 12 Eq. 2

n = 3:

9a + 3b + c = 26 Eq. 3

Eq. 2 minus Eq. 1

3a + b = 8 Eq. 4

Eq. 3 minus Eq. 2

5a + b = 14 Eq. 5

Eq. 5 minus Eq. 4

2a = 6

a = 3

Plug in a = 3 into Eq. 4

3(3) + b = 8

b = -1

Plug in a = 3 and b = -1 into Eq. 1.

3 - 1 + c = 4

c = 2

Answer: a = 3, b = -1, c = 2