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Harmonic Harmony 2 (Posted on 2016-03-31) Difficulty: 3 of 5
The number of terms of a harmonic sequence is even.

The sum of the terms in the odd places (First term + Third Term + Fifth Term + ...and so on) is 2625, and:
The sum of the terms in the even places (Second Term + Fourth Term + Sixth Term + ... and so on) is 4224; and:

Given that the last term exceeds the first by 2205, then identify the terms of the said sequence.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Lateral thinking? (spoiler) | Comment 1 of 2
An increasing harmonic sequence must look like this:

                        k*{1/an, 1/an-1, 1/an-2,……………, 1/a1}

where the ai are in arithmetic progression and increasing with i.

I can’t believe that KS would expect us to ‘identify all the terms’
if there were more than, say, eight. Also, surely he would want
to keep things simple:

                        k*{1/8, 1/7, 1/6, …………, ½, 1}

His condition for the difference then gives 7k/8 = 2205 so that
k = 2520 and the terms are:

            {315, 360, 420, 504, 630, 840, 1260, 2520}

The other conditions seem to be satisfied!

Lateral thinking, or a retrospective view following an exhaustive
computer search? I’ll let you decide.

  Posted by Harry on 2016-04-02 16:42:36
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