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An arithmetic progression has a positive common difference. The ratio of the difference of the 4th and 8th term to the 15th term is 4/15 and the square of the difference of the 4th and the 1st term is 225. Which term of the series is 2015?

 Sep 22, 2020
 #1
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I only find one sequence that comes close to satisfying your conditions and it begins with:

 

36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.......etc.

 

The ratio of the difference between the 8th and the 4th terms and the 15th term is:

[43 - 39] / 50 =4 / 50 and NOT 4 / 15. The difference between the squares of the 4th term and the 1st term is:

39^2 - 36^2 =225.

 

If the above is correct, then 2015 will be the 1980th term.

 Sep 22, 2020
 #2
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I get the following:

 Sep 22, 2020

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