Question

Find three numbers in G.P. such that their sum is $35$ & product is $1000$.

Answer 1

Let the numbers in G.P be $a,ar,a{r}^2$

Given that $a+ar+a{r}^2=35$ and $a\times ar\times a{r}^2=1000$

$a(1+r+r^2)=35$ and $ar=10\Rightarrow a=\frac{10}{r}$

$\frac{10}{r}(1+r+r^2)=35$

$\Rightarrow 2r^2-5r+2=0\Rightarrow 2r^2-4r-r+2=0$

$(2r-1)(r-2)=0$

$r=\frac{1}{2}or2$

If $r=\frac{1}{2}$ then $a=20$ ....... $Asa=\frac{10}{\frac{1}{2}}=20$

The terms of G.P will be $20,20\times \frac{1}{2},20\times \frac{1}{2^2}$ i.e $20,10,5$

If $r=2$ then $a=5$

The terms of G.P will be $5,5\times 2,5\times 2^2$ i.e $5,10,20$