Question

Determine whether the given sequence is arithmetic or geometric, and then calculate and provide the corresponding constant difference (CD) or common ratio (CR).

800, 640, 512, 409.6, ...

Answer 1

sequence is geometric

Step-by-step explanation:

if the sequence is arithmetic, it will have a common difference between consecutive terms.

640 - 800 = - 160

512 - 640 = - 128

409.6 - 512 = - 102.4

the difference between consecutive terms is not constant

Thus the sequence is not arithmetic

If the sequence is geometric, it will have a common ratio between consecutive terms.

`(640)/(800)` = 0.8

`(512)/(640)` = 0.8

`(409.6)/(512)` = 0.8

There is a common ratio , thus the sequence is geometric

Answer 2

The given sequence is a geometric sequence with a common ratio (CR) of 0.8, as each term is consistently multiplied by this factor to produce the next term.

Step-by-step explanation:

To determine if the sequence is arithmetic or geometric, we need to look at the pattern in which the numbers change. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms.

Let's examine the given sequence: 800, 640, 512, 409.6, ...

Calculating the difference between the first two terms: 640 - 800 = -160. Now, let's calculate the next difference: 512 - 640 = -128. We notice the difference is not the same; thus, it is not an arithmetic sequence.

Let's now find the ratio between consecutive terms: 640 / 800 = 0.8. Next, let's calculate the consecutive ratio: 512 / 640 = 0.8. The ratio is consistent, indicating it is a geometric sequence with a common ratio (CR) of 0.8.