ANSWER
The 10th term of the sequence can be found using the formula,
[tex]a_{10} =(x - 1)( - 2) ^{ 10- 1} [/tex]
EXPLANATION
The first four terms of the geometric sequence were given as,
[tex](x-1),(-2x+2),(4x-4),(-8x+8)[/tex]
We can determine the common ratio using any two subsequent terms.
The common ratio is,
[tex]r= \frac{ - 2x + 2}{x - 1} [/tex]
This implies that,
[tex]r= \frac{ - 2(x - 1)}{x - 1} = - 2[/tex]
Also, the first term of the sequence is,
[tex]a_1=x - 1[/tex]
The general term of the sequence is given by,
[tex]a_n=a_1(r) ^{ n- 1} [/tex]
We substitute the first term, the common ratio and [tex] n= 10[/tex]
in to the general term to get,
[tex]a_{10} =(x - 1)( - 2) ^{ 10- 1} [/tex]
The correct answer is option A.
