Geometric sequence question?

Question

The first, second and third terms of a geometric sequence are:

x+5, x and x-4 respectively. Find the value of x.

I got t1 = a = x+5

t2 = ar =x

t3 = ar^2 = x-4

However the answer's first step is: x^2 = (x+5)(x-4)

I'm just confused about the methodology. :(

Any help is appreciated. Thanks very much!

PS. x = 20

Answer 1

A geometric sequence means that the ratio between each term is constant, so we conclude that:

(x + 5) / x = x / (x - 4)

(x - 4)(x + 5) = x^2

x^2 + x - 20 = x^2

x - 20 = 0

x = 20

Answer 2

From this, x^2 = (x+5)(x-4)

you can get x

x^2=x^2-4x+5x-20

x^2=x^2+x-20

20=X^2-X^2 +x

therefore, x=20

hope this helps. =]

Answer 3

if r is the ratio

x=r(x+5) and

(x-4)=r(x)+so dividing

x/(x-4)= (x+5)/x so x^2 = x^2 +x-20 so x= 20 and r= 20/25=4/5

Answer 4

In fact you don't have to find a and r. Therefore u can reach result quicker.

In a geometric sequence a, ar, ar^2,... any term is a mean geometric of its nearest neighbors.

ar^n=sqrt( a*r^(n-1))(a*r^(n+1))

x^2=(x+5)(x-4)

x^2=x^2+x-20

x=20

This way you don't need even to denote a and r

Answer:x=20