Question

What is the nth term rule of the quadratic sequence below?

−
5
,
−
3
,
3
,
13
,
27
,
45
,
67
,
.
.
.

Answer 1

Explanation:

y=ax²+bx+c

x=1,y=-5

-5=a+b+c ...(1)

x=2,y=-3

-3=4a+2b+c ...(2)

x=3,y=3

3=9a+3b+c ...(3)

(2)-(1) gives

2=3a+b ...(4)

(3)-(2) gives

6=5a+b ...(5)

(5)-(4) gives

4=2a

a=4/2=2

from (4)

6=5(2)+b

b=6-10=-4

from (1)

-5=2+(-4)+c

-5=-2+c

c=-3

y=2x²-4x-3