Answered

Which sequences are geometric sequences?
Check all that apply.


4, 2, 1, 1/2,1/4,...

−2, 3, −4, 5, −6, …

2, 6, 18, 54, 162, …

−4, −16, −64, −256, …

−2, −4, −12, −48, −240, …

Verified Answer :

1.) 4, 2, 1, 1/2,1/4,...  2.) 2, 6, 18, 54, 162, …   3.) −4, −16, −64, −256, …  are geometric sequences because common ratio is same. Example: 1.) ratio of 1st and 2nd term is 1/2. similarly ratio of 3rd and 4th term is 1/2 and so on. 

Answer:

4, 2, 1, 1/2,1/4,...

2, 6, 18, 54, 162, …

−4, −16, −64, −256, …

Step-by-step explanation:

A geometric sequence is defined as a sequence formed by a factor, that is, a number which multiplied with an element form the next one.

For example, the sequence 4, 2, 1, 1/2,1/4,... is a geometric sequence, where the facor is 1/2, notice that each term is half that the previous one.

\(\frac{4}{2}=2\\\frac{2}{2}=1\\\)

And so on.

The other geomtric sequences are 2, 6, 18, 54, 162, … and −4, −16, −64, −256, …., the first one has a factor of 3 and the second has a dactor of 4.

Therefore, the right choices are the first, third and the fourth choices.

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