2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Sequence & Series

JEE Main & Advanced Mathematics Sequence & Series Question Bank Relation between AP., GP. and HP.

  • question_answer
    If \[a,\ b,\ c\] are in A.P. and \[|a|,\ |b|,\ |c|\ <1\] and \[x=1+a+{{a}^{2}}+........\infty \]\[y=1+b+{{b}^{2}}+.......\infty \]\[z=1+c+{{c}^{2}}........\infty \] Then\[x,\ y,\ z\] shall be in [Karnataka CET 1995; AIEEE 2005]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: C

    Solution :

    Clearly \[x=\frac{1}{1-a},\ y=\frac{1}{1-b},\ z=\frac{1}{1-c}\] Since \[a,\ b,\ c\] are in A.P. \[\Rightarrow \] \[1-a,\ 1-b,\ 1-c\] are also in A.P. \[\Rightarrow \] \[\frac{1}{1-a},\ \frac{1}{1-b},\ \frac{1}{1-c}\]are in H.P. \[\therefore \]\[x,\ y,\ z\] are in H.P.


You need to login to perform this action.
You will be redirected in 3 sec spinner