Question

Insert two numbers between 3 and 81 so that the resulting sequences is G.P.

Answer 1

Let $G_{1}and{G}_2$ be two numbers between 3 and 81 much that 3, $G_1,G_2$, 81 are in G.P.

Here, $a=3and{a}_4$ 81

Let 'r' be the common ratio of the given G.P

Then $a{r}^3=81\Rightarrow 3r^3=81$

$\Rightarrow r^3=27\Rightarrow r=3$

$\therefore G_1=ar=3\times 3=9$

$G_2=a{r}^2=3\times (3{)}^2=27$

Thus, 9 and 27 are required numbers between 3 and 81.