Question

Consider the first four terms of the sequence below. 1, -1/2,1/4,-1/8. What is the 8th term of this sequence?

A. 1/256
B. 1/128
C. -1/256
D. -1/128

Answer 1

the answer is D -1/128

Answer 2

Answer: D.
`(-1)/(128)`

Explanation:

The given geometric sequence : 1, -1/2, 1/4, -1/8

Here the first term=
`a=1`

Second term =
`ar=(-1)/(2)`, where r is the common ratio.

Therefore, the common ratio of the given sequence =
`r=(-1)/(2)`

The nth term of the geometric sequence is given by ;-

`ar^(n-1)`

Now, the 7th term of the geometric sequence is given by :-

`(1)((-1)/(2))^(8-1)=((-1)/(2))^7=(-1)/(128)`