Question

PLEASE HURRY !!!

Which sequences are geometric? Select three options.
A. -2.7, -9, -30, -100...
B. -1, 2.5, -6.25, 15.625...
C. 9.1, 9.2, 9.3, 9.4...
D. 8, 0.8, 0.08, 0.008...
E. 4, -4, -12, -20...

Answer 1

Sequences A (-2.7, -9, -30, -100...), B (-1, 2.5, -6.25, 15.625...), and D (8, 0.8, 0.08, 0.008...) are geometric, as they have consistent common ratios between the terms.

Step-by-step explanation:

The question asks which sequences are geometric. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For a sequence to be geometric, you can divide any term by the previous term, and the result which is the common ratio, should be constant. Let's evaluate the given sequences.

• A. -2.7, -9, -30, -100... (Geometric): To find the common ratio, divide the second term by the first term: -9 / -2.7 = 3.33, and the third term by the second: -30 / -9 ≈ 3.33. Since the ratio is consistent, this is a geometric sequence.
• B. -1, 2.5, -6.25, 15.625... (Geometric): Here, the ratio is -2.5 (e.g., 2.5 / -1), and -2.5 again (-6.25 / 2.5). Since the ratios are the same, this sequence is also geometric.
• C. 9.1, 9.2, 9.3, 9.4... (Not geometric): This sequence is not geometric because the difference is constant, which defines an arithmetic sequence, not geometric.
• D. 8, 0.8, 0.08, 0.008... (Geometric): The common ratio is 0.1 (e.g., 0.8 / 8), so it is a geometric sequence.
• E. 4, -4, -12, -20... (Not geometric): This sequence is not geometric because there isn't a consistent ratio between the terms.

Answer 2

A. -2.7, -9, -30, -100... ; B. -1, 2.5, -6.25, 15.625... ; D. 8, 0.8, 0.08, 0.008...

Step-by-step explanation:

A geometric sequence is one in which each term is found by multiplying each term by a constant, called the common ratio.

In sequence A, we can see that we do not add the same amount each time to find the next term; there is more difference between -2.7 and -9 than between -9 and -30.

Dividing, we find that -9/(-2.7) = 3.333333 = 3 1/3. This means that we multiply -2.7 by 3 1/3 to get 3. If we then multiply -9 by 3 1/3, we get

-9/1 * 3 1/3 = -9/1 * 10/3 = -90/3 = -30. Multiplying -30 by 3 1/3, we get

-30 * 3 1/3 = -30/1 * 10/3 = -300/3 = -100. This means A is geometric.

In sequence B, we see that multiplying -1 by -2.5 gives us 2.5. Multiplying 2.5 by -2.5 gives us -6.25; then multiplying -6.25 by -2.5 gives us 15.625. This means B is geometric.

In sequence C, we see that we would add 0.1 to each term to find the next. This is not geometric.

In sequence D, we see that multiplying 8 by 0.1 gives us 0.8. Multiplying 0.8 by 0.1 gives us 0.08; then multiplying 0.08 by 0.1 gives us 0.008. This is geometric.

In sequence D, we would multiply 4 by -1 to make -4; but then we would multiply -4 by 3 to make -12. This is not geometric.