SOLUTION: Find the 20th term of a HP.of which the first two terms are 2/39 and 2/37

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Question 1043665: Find the 20th term of a HP.of which the first two terms are 2/39 and 2/37
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Who is HP?

Hewlett-Packard?


Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
A harmonic progression is a sequence of quantities whose reciprocals are in arithmetic progression.
Since h%5B1%5D+=+2%2F39 and h%5B2%5D+=+2%2F37, it follows that a%5B1%5D+=+39%2F2 and a%5B2%5D+=+37%2F2.
===> d+=+37%2F2+-+39%2F2+=+-2%2F2+=+-1
===> a%5B20%5D+=+a%5B1%5D+%2B+%2820-1%29%2A-1+=+39%2F2+%2B+19%2A-1+=+1%2F2
Therefore the twentieth term of the harmonic progression is h%5B20%5D+=+2.