Question

Find the value of $x+y+z$ if $1,x,y,z,16$ are in $G.P$.

Answer 1

The $G.P$ series : $a,ar,a{r}^2,a{r}^3,a{r}^4$

$1,x,y,z,16$

$a=1$

$a{r}^4=16;r^4=16$

$r=\pm 2$

$ar=1\left(2\right)=2$

$ar=1(-2)=-$

$a{r}^2=1(+2{)}^2=4$

$a{r}^2=1(-2{)}^2=4$

$a{r}^3=1(2{)}^3=8$

$a{r}^3=1(-2{)}^3=-8$

$x,y,z=(2,4,8)$

$x,y,z=(-2,4,-8)$

$\therefore x+y+z\Rightarrow 14$ or $-6$