Question

If $x,x+2,x+3$ are consecutive terms of a $G.P$,then find $x$

Answer 1

Given: $x,x+2,x+3$ are consecutive terms of a G.P

To find :$x$

Solution: Since in a G.P the ratio between any two consecitive terms remains same

for the given three consecutive terms

$\frac{x+3}{x+2}=\frac{x+2}{x}$

$x(x+3)={(x+2)}^2$

$x^2+3x=x^2+4+4x$

$3x-4x=4$

$-x=4$

$x=-4$