In this investigation I am trying to find a rule for the difference between any consecutive numbers in a sequence. I am going to use a series of algebraic expressions to try and come up with a successful rule that works for every consecutive number I try.

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Math's Investigation

Consecutive Numbers

Introduction

In this investigation I am trying to find a rule for the difference between any consecutive numbers in a sequence. I am going to use a series of algebraic expressions to try and come up with a successful rule that works for every consecutive number I try.

2 Consecutive Numbers

1,2 = 3

2,3 = 5

3,4 = 7

4,5 = 9

3 Consecutive Numbers

1,2,3 = 6

2,3,4 = 9

3,4,5 = 12

4,5,6 = 15

4 Consecutive Numbers

1,2,3,4 = 10

2,3,4,5 = 14

3,4,5,6 = 18

4,5,6,7 = 22

As you can see from these results if I carry on the difference goes up by 4 each time.

5 Consecutive Numbers

1,2,3,4,5 = 15

2,3,4,5,6 = 20

3,4,5,6,7 = 25

4,5,6,7,8 = 30

Difference goes up by 5 each time.

6 Consecutive Numbers

1,2,3,4,5,6 = 21

2,3,4,5,6,7 = 27

3,4,5,6,7,8 = 33

4,5,6,7,8,9 = 39

Difference goes up by 6 each time.

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