Question

I NEED HELP PLEASE!

Khalid wrote the sequence below.
x-1, -2x+2, 4x-4, -8x+8
Which formula can be used to find the 10th term of the sequence?
A.
`a10=(x-1)*(-2)^1^0^-^1`
B.
`a10=(x-1)^1^0^-^1`
C.
`a10=(x-1)*(2)^1^0^-^1`
D.
`a10=(x-1)*(-2)^1^0`

Answer 1

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 =
`(a_(2))/(a_(1))`

=
`(-2x+1)/(x-1)`

=
`(-2(x-1))/((x-1))`Take out -2 as common factor

= -2 Cancel out x - 1.

The formula for general term of a geometric sequence is,

`a_(n) =a_(1) r^(n-1)`

Where, first term:
`a_(1) =x-1`

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,

`a_(10) = (x -1)(-2)^(10-1)`

So, A is the correct choice.