Q99 / 160 · WBJEE 2011 · Mathematics

The sequence \(\log \mathrm{a}, \log \frac{\mathrm{a}^2}{\mathrm{~b}}, \log \frac{\mathrm{a}^3}{\mathrm{~b}^2}, \ldots \ldots \ldots\). is

  • A
    a GP.
  • Correct answer
    B
    an A.P.
  • C
    a H.P.
  • D
    both a G.P. and a H.P

Solution

\(\begin{aligned}\text {Hints: } & \log \mathrm{a} \cdot(2 \log \mathrm{a}-\log \mathrm{b})(3 \log \mathrm{a}-2 \log \mathrm{b}) \\ & =\mathrm{T}_2-\mathrm{T}_1=\log \mathrm{a}-\log \mathrm{b} \\ = & \mathrm{T}_3-\mathrm{T}_2=\log \mathrm{a}-\log \mathrm{b} \end{aligned}\)

Hence, the correct answer is option: 'B'.

Relevant Questions