Question

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

Answer 1

Answer:

We have been given that  numbers between 3 and 24

So, let the two numbers be a and b

3,a,b,24

So, the first term is a=3 and fourth term that is $ar^{n-1}=ar^3=24$

In GP the ratio between consecutive terms is same

So, $\frac{a}{3}=\frac{24}{b}$

$ab=72$

$b=ar^2$ being the third term.

$ar^3=24$

Since, a=3

$r^3=8$

r=2

And a=3

So, $ar=3\cdot 2=6$ is the second number.

And $ar^2=3\cdot 4=12$ is the other number.