Question

Which sequences are geometric? Check all that apply.

–2.7, –9, –30, –100, ...


–1, 2.5, –6.25, 15.625, ...


9.1, 9.2, 9.3, 9.4, ...


8, 0.8, 0.08, 0.008, ...


4, –4, –12, –20, ...

Answer 1

The answers are A, B, and D

Explanation:

these are geometric

Answer 2

–2.7, –9, –30, –100, ...

–1, 2.5, –6.25, 15.625, ...

8, 0.8, 0.08, 0.008, ...

Explanation:

A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

now check all the sequence one by one.

For sequence –2.7, –9, –30, –100, ...

r =
`(-9)/(-2.7)=  3.333`

=
`(-30)/(-9)  = 3.3333`

=
`(-100)/(-30) = 3.3333`

We see that, all the ratios are same.

So this is geometric sequence.

For sequence –1, 2.5, –6.25, 15.625, ...

r =
`(2.5)/(-1)  =  (-6.25)/(2.5)  = (15.625)/(-6.25)  = 2.5`

This is also geometric sequence.

For sequence 9.1, 9.2, 9.3, 9.4, ...

In this sequence, common ratio is not same.

So, it is not a geometric sequence.

For sequence 8, 0.8, 0.08, 0.008, ...

Common ratio is same so, it is geometric sequence.

For sequence 4, –4, –12, –20, ...

Common ratio is not same. So, it is not geometric sequence .