consecutive integers consecutive integers are integers that follow one after another. example 1: are...

Consecutive Integers

Consecutive Integers are integers that follow one after another.

Example 1:

8, 9,10,11, ...

are consecutive integers.

In Algebra we sometimes are presented with a problem that requires a pattern of consecutive integers.

The patterns are usually one of three types:

1) Consecutive Integers

2) Consecutive Even Integers

3) Consecutive Odd Integers

Add 2 to the 8 to get the next integer 10:

Consecutive Integers

Consider the example given earlier:

8, 9,10,11, ...

Given the first integer 8, what would be necessary to determine the next integer of 9?

Simply add 1 to the 8 to give:

8 1 9

8 2 10

Let x represent the first integer.

Consecutive Integers

What if the first integer is unknown?

Simply add 1 to get the second integer.

x

, 1x x

Add 2 to get the third integer.

, 1, 2x x x

Consecutive Integers

Assume that we are considering three consecutive integers, and do not know the first integer.

The pattern is given by:

Example 2: Now assume that we know the first integer is 17. The integers are …

, 1, 2x x x

17,17 1,17 2

17,18,19

Consecutive Even Integers:

Consecutive Even Integers

Consecutive Odd Integers

Consecutive even integers and consecutive odd integers will be considered together since they are related.

6, 8,10, ...

7, 9,11, ...Consecutive Odd Integers:

Consecutive Even Integers

Consecutive Odd Integers

Notice the common pattern for the second integer:

6, 8,10, ... 7, 9,11, ...

Increase by 2 Increase by 2

Consecutive Even Integers

Consecutive Odd Integers

Notice the common pattern for the third integer:

6, 8,10, ... 7, 9,11, ...

Increase by 4 Increase by 4

Note that it is the first integer that determines the pattern of even or odd.

Assume that we are considering

three consecutive even integers, or

three consecutive odd integers,

and do not know the first integer.

Both patterns are given by:

, 2, 4, ...x x x

Consecutive Even Integers

Consecutive Odd Integers

Example 3:

Write the pattern for three consecutive odd integers:

, 2, 4x x x

Determine the integers if the first integer is -7:

7, 7 2, 7 4

7, 5, 3