A) \[\frac{1}{89}\]
B) \[\frac{1}{85}\]
C) \[\frac{1}{81}\]
D) \[\frac{1}{77}\]
Correct Answer: A
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\[=\frac{1}{89}\]
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