Presentation on theme: "Consecutive Integers Consecutive Integers are integers that follow one after another. Example 1: are consecutive integers."— Presentation transcript:
1Consecutive IntegersConsecutive Integers are integers that follow one after another.Example 1:are consecutive integers.
2In 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 Integers2) Consecutive Even Integers3) Consecutive Odd Integers
3Consecutive IntegersConsider the example given earlier:Given the first integer 8, what would be necessary to determine the next integer of 9?Simply add 1 to the 8 to give:Add 2 to the 8 to get the next integer 10:
4Consecutive IntegersWhat if the first integer is unknown?Let x represent the first integer.Simply add 1 to get the second integer.Add 2 to get the third integer.
5Consecutive IntegersAssume 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 …
6Consecutive Even Integers Consecutive Odd Integers Consecutive even integers and consecutive odd integers will be considered together since they are related.Consecutive Even Integers:Consecutive Odd Integers:
7Consecutive Even Integers Consecutive Odd Integers Notice the common pattern for the second integer:Increase by 2Increase by 2
8Consecutive Even Integers Consecutive Odd Integers Notice the common pattern for the third integer:Increase by 4Increase by 4Note that it is the first integer that determines the pattern of even or odd.
9Consecutive Even Integers Consecutive Odd Integers Assume that we are consideringthree consecutive even integers, orthree consecutive odd integers,and do not know the first integer.Both patterns are given by:
10Example 3:Write the pattern for three consecutive odd integers:Determine the integers if the first integer is -7: