The given sequence is x-1, -2x+2, 4x-4, -8x+8 .
Notice that this is a geometric sequence because here we have equal common ratio.
So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]
= [tex] \frac{-2x+1}{x-1} [/tex]
= [tex] \frac{-2(x-1)}{(x-1)} [/tex]Take out -2 as common factor
= -2 Cancel out x - 1.
The formula for general term of a geometric sequence is,
[tex] a_{n} =a_{1} r^{n-1} [/tex]
Where, first term: [tex] a_{1} =x-1 [/tex]
We need to find the 10th term of this sequence. So, n = 10.
Next step is to plug in these values in the above formula to get the 10th term. Hence,
[tex] a_{10} = (x -1)(-2)^{10-1} [/tex]
So, A is the correct choice.
