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# help

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

Aug 3, 2020

#1
+783
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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
+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
+783
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good job, looks like i was a little off...

gwenspooner85  Aug 3, 2020
#4
+28021
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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