Thread: Finding the median

The sum of 5 consecutive integers is 10n + 5. What is the median of the 5 integers in terms of n?

How can you prove that it must be 2n + 1?

Call the first of the consecutive integers "i". Then the next four integers are i+1, i+2, i+3, and i+4. The sum of those five numbers is i+ (i+1)+ (i+ 3)+ (i+ 4)+ (i+ 5)= 5i+ 10= 10n+ 5. Solve that for i in terms of n. The "median" is the middle number, i+ 2.

How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.

Originally Posted by HallsofIvy

Call the first of the consecutive integers "i". Then the next four integers are i+1, i+2, i+3, and i+4. The sum of those five numbers is i+ (i+1)+ (i+ 3)+ (i+ 4)+ (i+ 2)= 5i+ 10= 10n+ 5. Solve that for i in terms of n. The "median" is the middle number, i+ 2.

Originally Posted by dannyc

The sum of 5 consecutive integers is 10n + 5. <--- your own words. Remember?
What is the median of the 5 integers in terms of n?

How can you prove that it must be 2n + 1?

Originally Posted by dannyc

How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.

You are supposed to know what a median means or is.

In your case the median is the 3rd term, that means (i + 2). Since i = 2n - 1 the term i + 2 = 2n + 1.

Right, but I still do not know how we can set i + 2 = 2n + 1. Why can that conclusion be made algebraically?

Originally Posted by dannyc

Right, but I still do not know how we can set i + 2 = 2n + 1. Why can that conclusion be made algebraically?

1.







Now add 2 on both sides of this equation:

Originally Posted by dannyc

How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.

I don't know what you mean by "implies" here. I said they were equal and that is true because YOU said it was:
"The sum of 5 consecutive integers is 10n + 5".