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The 8th and 14th term of a H.P. are 1/2 ...

The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find its 20th term. Also, find its general term.

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The correct Answer is:
20 th term =1/4 general term `=6/(n+4)`
Let the H.P. be `1/a,1/(a+d),1/(a+2d),…,1/(a+(n-1)d),…,1/(a+(n-1)d,…`
Then, `a_(8)=1/2 and a_(14)=1/3`
`rArr1/(a+7d)=1/2`
and `1/(a+13 d)=1/3` `[because a_(n)=1/(a+(n-1)d)]`
`rArra+7d=2 and a+13d=3`
`rArra=5/6,d=1/6`
Now, `a_(20)=1/(a+19d)=1/(5/6+19/6)=1/4`
and `a_(n)=1/(a+(n-1)d)=1/(5/6+(n-1)xx1/6)=6/(n+4)`
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