Here are the first four terms of a quadratic sequence. The nth term of this sequence is an² + bn + c.
1, 11, 27 and 49
Find the values of a, b and c.

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

Step-by-step explanation:

Substitute n = 1, 2, 3 into the n th term

a + b + c = 1 → (1)

4a + 2b + c = 11 → (2)

9a + 3b + c = 27 → (3)

Subtract (1) from (2) term by term to eliminate c

Subtract (2) from (3) term by term to eliminate c

3a + b = 10 → (4)

5a + b = 16 → (5)

Subtract (4) from (5) term by term to eliminate b

2a = 6 ( divide both sides by 2 )

a = 3

Substitute a = 3 into (4) and evaluate for b

3(3) + b = 10

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

b = 1

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

3 + 1 + c = 1

4 + c = 1 ( subtract 4 from both sides )

c = - 3

Then a = 3, b = 1 and c = - 3

translate k to n and reflect across the line containing jk.