Determine whether this sequence is arithmetic or geometric. Find the next three terms.

81, 27, 9, 3, . . .
A. arithmetic, 0, –3, –6
B. geometric, 0, –3, –6
C. geometric, 1,1/3 , 1/9
D. The sequence is neither geometric nor arithmetic.
Is the answer C?
Thank you

Yes. The common ratio is 1/3 the previous term.

Thank you sooooooo much Irving.

No Problem. Glad I could help.

Tell whether the sequence 1/3,0,1,-2 is arithmetic, geometric, or neither. Find the next three terms of the sequence.

A.neither;7,-20,61
B.geometric;7,-20,61
C.arithmetic;1/3,1 1/3,3
D.geometric;-3 1/3, 5 5/9,9 7/27

1. C

2. B
3. C
4. B
5. D

ur welcome

To determine whether the sequence is arithmetic or geometric, we need to look for a consistent pattern in the differences or ratios between the terms.

Let's examine the given sequence: 81, 27, 9, 3, ...

To check for arithmetic progression, we calculate the differences between consecutive terms:

27 - 81 = -54
9 - 27 = -18
3 - 9 = -6

The differences are not constant, so the sequence is not arithmetic.

Now let's check for a geometric progression by calculating the ratios:

27 ÷ 81 = 1/3
9 ÷ 27 = 1/3
3 ÷ 9 = 1/3

The ratios are constant (1/3), which means the sequence is geometric.

Now, to find the next three terms, we can simply continue the pattern:

3 ÷ 1/3 = 9
9 ÷ 1/3 = 27
27 ÷ 1/3 = 81

So, the next three terms in the sequence are 9, 27, and 81.

Option C, geometric with the terms 1, 1/3, and 1/9, matches the pattern we found for the sequence. Therefore, the answer is C.

Remember, to determine whether a sequence is arithmetic or geometric, examine the differences or ratios between terms.