Question

Determine whether or not each of the following sequences is a geometric sequence. Check all that apply.

-48, 96, -192, 384, …
1, 4, 9, 16, ...
3, 9, 27, 81, …
5, 10, 20, 40, …
24, 20, 16, 12, …
25, 20, 15, 10, …

Answer 1

1, 3, and 4

Explanation:

We know that a geometric sequence is a sequence of numbers that is in a pattern where the next term is obtained by multiplying by a constant known as the common ratio.

1. -48, 96, -192, 384

here,

hence, it is a geometric sequence.

2. … 1, 4, 9, 16

here,

hence, it is not a geometric sequence.

3. ... 3, 9, 27 81 …

here,

hence, it is a geometric sequence.

4. 5, 10, 20, 40, …

here,

hence, it is a geometric sequence.

5. 24, 20, 16, 12, …

here,

hence, it is not a geometric sequence.

6. 25, 20, 15, 10, …

here,

hence, it is not geometric sequence.

Answer 2

-48, 96, -192, 384, …

3, 9, 27, 81, …

5, 10, 20, 40, …

Explanation:

We know that a geometric sequence is a sequence of numbers that is in a pattern where the next term is obtained by multiplying the previous term by a constant known as the common ratio.

-48, 96, -192, 384,...

here, the next term is obtained by multiplying the previous term by -2

Hence, it is a geometric sequence.

1, 4, 9, 16,...

It is not a geometric sequence.

3, 9, 27 81, …

here, the next term is obtained by multiplying the previous term by 3

Hence, it is a geometric sequence.

5, 10, 20, 40, …

here, the next term is obtained by multiplying the previous term by 2

Hence, it is a geometric sequence.

24, 20, 16, 12, …

It is not a geometric sequence.

25, 20, 15, 10, …

It is not geometric sequence.