Question

Given the sequence 128, −32, 8… , which of the following statements is TRUE? *

A. The sequence is a geometric sequence with a common ratio of −4.
B. The sequence is an arithmetic sequence with a common difference of −4.
C. The sequence is a geometric sequence with a common ratio of -1/4.
D. The sequence is an arithmetic sequence with a common difference of -1/4

Answer 1

C

Explanation:

The sequence has a common ratio r between consecutive terms

r =
`(a_(2) )/(a_(1) )` =
`(-32)/(128)` = -
`(1)/(4)`

r =
`(a_(3) )/(a_(2) )` =
`(8)/(-32)` = -
`(1)/(4)`

Thus the sequence is geometric with common ratio r = -
`(1)/(4)`

Answer 2

C

Explanation:

Because the ratio between 128 and -32 is the same as the ratio between -32 and 8