Answer:
x = 8
Step-by-step explanation:
This sequence is a geometric sequence.
As it is a geometric sequence, It means that each term multiply by a value that we call that value "a".
So (x-4) × a = (x + 2)
Therefore [tex]\frac{x+2}{x-4} = a[/tex]
And (x+2) × a = (3x+1)
Therefore [tex]\frac{3x+1}{x+2} =a[/tex].
By this we can make a conclusion that [tex]\frac{3x+1}{x+2} =\frac{x+2}{x-4}[/tex].
- [tex]\frac{3x+1}{x+2}= \frac{x+2}{x-4}[/tex]
- [tex](3x + 1) * (x-4) = (x+2) * (x+2)[/tex]
- [tex]3x^{2} -11x-4=x^{2} +4x+4[/tex]
- [tex]2x^{2} -15x-8 = 0[/tex]
- [tex](2x+1) * (x-8) = 0[/tex]
In the last part one of the parentheses should be 0.
First we put (2x+1) equal to 0.
- [tex]2x+1 = 0[/tex]
- [tex]2x = -1[/tex]
- [tex]x = -\frac{1}{2}[/tex]
It gives us a negative answer, so this is not our answer.
Now we put (x-8) equal to 0.
- [tex]x-8=0[/tex]
- [tex]x = 8[/tex]
This is a positive answer and it is correct.
and the terms are 4, 10, 25 , ...
Please choose my answer as the brainliest answer.
