Answer:
x=0 or x=3
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