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The sum of 27 consecutive positive integers is \(3^7\). What is their median?

 Aug 3, 2020
 #1
avatar+783 
+2

The sum of 27 conescutive integers is 3^7 or 2187.

 

We write an equation x+(x+1)+(x+2)+...(x+26)=2187 and solve for x.

 

x+(x+1)+(x+2)+...(x+26)=2187

27x+351=2187

27x=1836

x=68.

 

The median is x+12, so the median is 68+12=80.

 Aug 3, 2020
 #2
avatar+18 
0

I tried it then realized that the median of a set of consecutive positive integers is equal to the mean of the set of integers so therefore it was:

\(\frac{3^7}{3^3}=81\)

 

thanks for helping me get the answer :D

 Aug 3, 2020
 #3
avatar+783 
+4

good job, looks like i was a little off...

gwenspooner85  Aug 3, 2020
 #4
avatar+28021 
+1

You did good GS....it is just that the median is   x + 13     (the 14th number in the 27 number sequence )

ElectricPavlov  Aug 3, 2020

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