Determine the value of x if the sequence 2x-1; 3x+1; 7x-1; is a geometric sequence

x=0 or x=3

Step-by-step explanation:

Since it is a geometric sequence, that means term divided by previous term is the same number. Let's call that number, r.

That means we have:

(3x+1)/(2x-1)=r

(7x-1)/(3x+1)=r

Since both of the ratios are the same, then we have

(3x+1)/(2x-1)=(7x-1)/(3x+1)

Cross multiply:

(3x+1)(3x+1)=(2x-1)(7x-1)

Distribute:

9x^2+3x+3x+1=14x^2-2x-7x+1

Combine like terms:

9x^2+6x+1=14x^2-9x+1

Subtract 1 on both sides:

9x^2+6x=14x^2-9x

Subtract 14x^2 on both sides

Add 9x on both sides

-5x^2+15x=0

Factor -5x:

-5x(x-3)=0

-5x=0 when x=0 since -5(0)=0

x-3=0 when x=3 since 3-3=0

y-y2 <6x+3x+x-12

y>9x-12