Question

Insert two numbers between $3$ and $24$ so that the resulting sequence is a G.P.

Answer 1

Let the 2 numbers be a,b.

$\therefore 3,m,n,24$ are G.P.

$m=ar,n=a{r}^2$

$3=a$

$24=a{r}^3$

$24=3\times r^3$

$8=r^3$

$\therefore r=2$

$m=ar=3\times 2=6$

$n=a{r}^2=3\times 2^2=12$