JEE Main & Advanced
Mathematics
Sequence & Series
Question Bank
Harmonic Progression
question_answer
If sixth term of a H.P. is \[\frac{1}{61}\] and its tenth term is \[\frac{1}{105},\] then first term of that H.P. is [Karnataka CET 2001]
A)\[\frac{1}{28}\]
B)\[\frac{1}{39}\]
C)\[\frac{1}{6}\]
D)\[\frac{1}{17}\]
Correct Answer:
C
Solution :
of H.P. \[=\frac{1}{61}\,\Rightarrow {{T}_{6}}\] of A.P. = 61 and of H.P. \[=\frac{1}{105}\Rightarrow \,{{T}_{10}}\] of A.P. = 105, so \[a+5d=61\] .......(i) and \[a+9d=105\] ?..(ii) From (i) and (ii),\[a=6\] Therefore first term of H.P.\[=\frac{1}{a}=\frac{1}{6}\].