Question

Which of the following are geometric sequences?

Check all that apply.

A. 10, 5, 2.5, 1.25, 0.625, 0.3125
B. 5, 10, 15, 20, 25
C. -9, -3, -1, -1/3, -1/9, -1/27
D. 1, 1, 2, 3, 5, 8, 13

Answer 1

A

C

Step-by-step explanation:

Answer 2

Answer: Option A and C

Step-by-step explanation:

the geometric sequence is the sequence in which ratio of all consecutive terms is equal for example ratio of third term to the second term is equal to the ratio of second term to the first term.

Here are some general terms of geometric sequence a,ar,
`ar^(2)`.........
`ar^(n-1)`.

In option A when
`(5)/(10) =(1)/(2)` ,
`(2.5)/(5) =(1)/(2)`,
`(1.25)/(2.5) =(1)/(2)` ,
`(0.625)/(1.25) =(1)/(2)` and
`(0.3125)/(0.625) =(1)/(2)` follow the rule of geometric sequence

In option B when
`(10)/(5) =2` ,
`(15)/(10) =(3)/(2)` does not follow the rule of geometric sequence

In option C when
`(-3)/(-9) =(1)/(3)` ,
`(-1)/(-3) =(1)/(3)`,
`\frac{(-1)/(3)} {-1} =(1)/(3)` ,
`\frac{(-1)/(9)} {(-1)/(3)}=(1)/(3)` and
`((-1)/(27))/((-1)/(9))  =(1)/(3)` follow the rule of geometric sequence

In option D
`(1)/(1) =1`,
`(2)/(1) =2` does not follow the rule of geometric sequence.