Question

The first three terms of a geometric sequence are shown below.

What is the eighth term of the sequence?
A. -128x^8-384x^7
B. 128x^8+384x^7
C. 256x^9+768x^8
D. -256x^9-768x^8

Answer 1

This is a geometric sequence of the form:

a(n)=(x+3)(-2x)^(n-1) because each term is -2x times the previous term...so

a(8)=(x+3)(-128x^7)

a(8)=-128x^8-384x^7

Answer 2

`a_8=-128x^8-384x^(7)`

Explanation:

G.P. =
`x+3,-2x^2-6x,4x^3+12x^2+...`

So, first term = a=x+3

Common ratio =
`r =(a_2)/(a_1)`

=
`(-2x^2-6x)/(x+3)`

=
`(-2x(x+3))/(x+3)`

=
`-2x`

So, r = -2x

nth term of G.P. =
`a_n=ar^(n-1)`

Substitute n = 8

`a_8=(x+3)(-2x)^(8-1)`

`a_8=(x+3)(-2x)^(7)`

`a_8=(x+3)(-128)(x)^(7)`

`a_8=-128x^8-384x^(7)`

Hence the eighth term of the sequence is
`a_8=-128x^8-384x^(7)`