GCSE Mathematics/Quadratic Equations

2

   :   3   :   10   :   23

    1        7       13    first difference

       6          6        second difference

using the formula

2a= the second difference

2a= 6

a=3

From finding a, you then proceed to find b

3a+b=first difference

3(3)+b=1

9+b=1

b=-8

Finding c

a+b+c= first term

3+(-8)+c=2

-5+c=2

c=7

Substitute the values for a, b and c into

Tn=an*2+bn+c (the first n being to the power of 2)

Tn= 3n*2-8n+7