Consider a set of \(n\) consecutive terms from an arithmetic progression. Take any 2 terms and replace them by their average. Continue this until only one number remains. Prove that the mean of all end numbers (they need not be distinct) is equal to the median and, for \(n \geq 4\), the mode.

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TopNewestOh wow, wasn't expecting the mean, mode and median to be the same.

I guess that the first step is: "How many different ways are they to do this for \(n\) consecutive terms?" – Calvin Lin Staff · 1 year, 9 months ago

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In any triangle ABC prove that cosA+cosB+cosC<or=3/2 – Mr.ahmed Mostafa · 1 year, 9 months ago

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– Sharky Kesa · 1 year, 9 months ago

Is this, in any way, relevant to the question at hand? Please refrain from doing this.Log in to reply

– Keshav Tiwari · 1 year, 9 months ago

Sorry , even i shouldn't have replied to it.Log in to reply

– Keshav Tiwari · 1 year, 9 months ago

Well you just need to plot the graph and consider three points A,B and C. Take the centroid of the triangle and compare ordinates.Simple.Log in to reply