Question

Consider the following sequence. 8^5, 8^4, 8^3, 8^2, ____, ... (a) Classify the sequence as arithmetic, geometric, Fibonacci, or none of these. arithmetic geometric Fibonacci none of these Correct: Your answer is correct. (b) If arithmetic, give d; if geometric, give r; if Fibonacci, give the first two terms. (If Fibonacci, enter your answers as a comma-separated list. If none of these, enter NONE.) Incorrect: Your answer is incorrect. (c) Supply the next term.

Answer 1

The given sequence is a geometric sequence with a common ratio of 1/8. The next term in the sequence is 1.

Step-by-step explanation:

The sequence given is 85, 84, 83, 82, ____, ...

This is a geometric sequence since each term is obtained by multiplying the previous term by a constant ratio.

The common ratio (r) can be found by dividing any term by its previous term. For example, dividing 84 by 85 gives 1/8. So, the common ratio is 1/8.

The next term in the sequence can be found by multiplying the last term (82) by the common ratio (1/8). Therefore, the next term is (1/8) * 82 = 1.

Answer 2

The sequence is geometric and the common ratio (r) is 1/8

The next term is 8

Classifying the sequence

From the question, we have the following parameters that can be used in our computation:

8⁵, 8⁴, 8³, 8², ____,

We can see that each term in the sequence is obtained by multiplying the previous term by 1/8.

So, the sequence is geometric

Calculating the common ratio (r)

The common ratio (r) in a geometric sequence is the number by which we multiply each term to get the next term. In this case, r = 1/8.

The next term

To find the next term, we simply multiply the last term (8²) by r:

8² * 1/8 = 8

So, the completed sequence is: 8⁵, 8⁴, 8³, 8², 8