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Find the 1st term of a harmonic sequence whose 5th term is 1/28 and whose 13th term is 1/180.

 Oct 2, 2020
 #1
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The first term is -4/11.

 Oct 2, 2020
 #2
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1/28 =1 / [F + 4D]

1/180 = 1 /[F + 12D], solve for D, F

F = -48  and  D= 19

 

First term =1 /-48. The harmonic sequence looks like this:

1/-48,  1/-29,  1/-10,  1/9,  1/28,  1/47,  1/66,   1/85,   1/104,  1/123,  1/142,  1/161,  1/180.....etc.

 Oct 2, 2020

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