Question

If the terms of one geometric progression are multiplied by the corresponding terms of another geometric progression, the sequence obtained will be in

• A. AP
• B. HP
• C. GP
• D. AGP
• E. Can not be determined

Answer 1

Answer: (C)

GP

Let two GP are
$a,ar,a{r}^2,a{r}^3,a{r}^4.....$ and $b,bs,b{s}^2,b{s}^3,b{s}^4,.....$
Their multiplication is
$ab,\left(ar\right)\left(br\right),\left(a{r}^2\right)\left(b{r}^2\right),\left(a{r}^3\right)\left(b{r}^3\right),.......$
i.e. $ab,ab\left(rs\right),ab(rs{)}^2,ab(rs{)}^3,.......$
Clearly it is a GP with first term multiplication of first terms of both GP and common ratio is product of their common ratios.
Option C is correct.