A quadratic pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to -14

- Calculate the second difference of this quadratic pattern
- Hence, or otherwise, calculate the first term of the pattern.

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1. let 1st and 4th terms be x and y respectively,

1st difference= 1-x,-7,y+6,-14-y,..

2nd difference= x-8,y+13, -2y-20,...

since 2nd diff is constant,

x-8=y+13........1

y+13=-2y-20........2

then from 2, 3y=-33

y= -11

and subst to 1, x= -11+13+8= 10

hence 2nd difference= y+13= -11+13= 2

2. 1st term= x

= 10 , calculated in question 1.

1st difference= 1-x,-7,y+6,-14-y,..

2nd difference= x-8,y+13, -2y-20,...

since 2nd diff is constant,

x-8=y+13........1

y+13=-2y-20........2

then from 2, 3y=-33

y= -11

and subst to 1, x= -11+13+8= 10

hence 2nd difference= y+13= -11+13= 2

2. 1st term= x

= 10 , calculated in question 1.

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