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Q.
If 5th term and 11th term of a harmonic progression are $ \frac{1}{45} $ and $ \frac{1}{69} $ respectively, then 16th term is
Rajasthan PETRajasthan PET 2003
Solution:
Since, 5th and 11th terms of a harmonic progression are
$ \frac{1}{45} $ and $ \frac{1}{69} $ respectively,
therefore 5th and 11th terms of the corresponding AP are 45 and 69 respectively.
$ \therefore $ $ 45=a(5-1)d $
$ \Rightarrow $ $ 45=a+4d $ ...(i) and $ 69=a+10d $ ...(ii)
On solving Eqs. (i) and (ii), we get $ a=29,d=4 $
$ \therefore $ $ {{T}_{16}}=29+15\times 4=89 $
$ \therefore $ 16th term of harmonic progression $ =\frac{1}{89} $