Question

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, …

Answer 1

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 2

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

2, 6, 18, 54, 162, …

−4, −16, −64, −256, …

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.

`(4)/(2)=2\\(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.