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Write-up


Title
The Sum of Five positive consecutive odd numbers

Problem Statement
 The sum of five positive consecutive odd numbers is 3055. Find the least of these numbers.

YJB_ConsectiveNumber.htm

Problem setup

Find five positive odd numbers with the value of 3055. Of the five positive odd numbers which has the least value

Plans to Solve/Investigate the Problem

Problem was discussed in class several methods can be used to derive the answer

 

Investigation/Exploration of the Problem

 

Question? To begin how big is the 1st positive consecutive odd number

 

5/3000=600 odd number close to 600is 601

 

Trail & Error:

601+603+605+607+609+=3025

 

603+605+607+609+611=3035

 

605+607+609+611+613=3045

 

607+609+611+613+615=3055

 

The least of these numbers 607

 

Extensions of the Problem

1st Alternate method of solving the problem:

Find the middle value which is the average this works because the numbers are evenly spaced

 

3055/3= 611 (The median value)

607+609+611+613+615=3055

The least of these numbers 607

 

2nd Alternate method of solving the problem:

x=    1st consecutive positive odd number

x+2=2nd consecutive positive odd number

x+4=3rd  consecutive positive odd number

x+6=4th  consecutive positive odd number

x+8=5th  consecutive positive odd number

x+ x+2 +x + 4+x +x+6 +x+8=

5x=20=3055

5x=3055

x=607

The least of these numbers 607