Here are the first four terms of a quadratic sequence, the nth term of this quadratic sequence is an² + bn + c.
2, 12, 28, 50
Find the values of a, b and c.
(4 marks)​

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

Step-by-step explanation:

Substitute n = 1, 2, 3, 4 into the nth term and equate to the values , that is

a + b + c = 2 → (1)

4a + 2b + c = 12 → (2)

9a + 3b + c = 28 → (3)

16a + 4b + c = 50 → (4)

Subtract (1) from (2) to eliminate c

3a + b = 10 → (5)

Subtract (3) from (4) to eliminate c

7a + b = 22 → (6)

Subtract (5) from (6) to eliminate b

4a = 12 ( divide both sides by 4 )

a = 3

Substitute a = 3 into 5) and solve for b

3(3) + b = 10

9 + b = 10 ( subtract 9 from both sides )

b = 1

Substitute a = 3 and b = 1 into (1) and solve for c

3 + 1 + c = 2

4 + c = 2 ( subtract 4 from both sides )

c = - 2

Then

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

and y = 3n² + n - 2 ← explicit formula

49%

step-by-step explanation:

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