Question

if x-2,x,x+3are three elements of gp then X is​

Answer 1

a^2-a^1=d

x-(x-2)=d

x-x+2=d

d=2

Answer 2

Answer: The value of x is 6.

Step-by-step explanation:

Since we have given that

x-2, x, x+3 are in G.P.,

i.e. a, b,c.

So, they have common ratio i.e.

$\dfrac{b}{a}=\dfrac{c}{b}$

So, we know that

$b^2=ac$

so, our equation becomes,

$b^2=ac\\\\x^2=(x-2)(x+3)\\\\x^2=x^2+x-6\\\\0=x-6\\\\x=6$

Hence, the value of x is 6.