Question

The reciprocals of all the terms of a geometric progression form a ________ progression.

• A. AP
• B. AGP
• C. GP
• D. None of these

Answer 1

The correct option is C GP

Let $a$ be the first term and $r$ be the common ratio of the GP.

So, the series is $a,ar,a{r}^2...$

Their reciprocals are $\frac{1}{a},\frac{1}{ar},\frac{1}{a{r}^2}..$

It is also a GP, with first term $\frac{1}{a}$ and common ratio $\frac{1}{r}$