Question

1.1.
A quadratic pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to
- 14.
1.1.1. Calculate the second difference of this quadratic pattern.
(5)
​

Answer 1

The second difference of this quadratic pattern is 2.

The first term of this quadratic pattern is 10.

Quadratic pattern

A sequence of numbers has a quadratic pattern when its sequence of second differences is constant. Therefore,

let the first and fourth term be a and b.

Therefore,

first difference:

1 - a; - 6 - 1 = -7; b + 6; -14 - b;

Second difference:

The second difference is constant . Therefore,

-7  - (1 - a) = -8 + a; b + 6 + 7 = b + 13; -14 - b - b - 6 = -2b - 20;

Therefore,

b + 13 = -8 + a

b  - a = -21

Then,

-2b - 20  = b + 13

-3b = 33

b = 33 / -3

b = - 11

Therefore,

- 11 - a = - 21

-a = -21 + 11

-a = -10

a = 10

Hence, the second difference = b + 13 = -11 + 13 = 2

First term = a

Therefore,

a = 10

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