4. Which explains why the sequence 81, 3, 1/9,... is arithmetic or geometric?

A)The sequence is arithmetic because it decreases by a factor of 1/27
B)The sequence is geometric because it decreases by a factor of 1/27
C)The sequence is arithmetic because it decreases by a factor of 3.
D)The sequence is geometric because it decreases by the factor of 3.

The answer is b. because the number 81 is divided by 1/27 to get 3 and 3 divided by 1/27 is 1/9. If you really look at the statement I wrote you would see that 27 * 1/9 = 3.An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. In this sequence the difference between the consecutive terms isn't constant. So, the sequence is geometric.

Yes, the answer is B.

is it A?

no. what form is Ao* r^n ? You need to know that.

then its B

I guess it D Miranda

how about this, can someone actually be sure on one answer!?! I mean "I guess", doesn't mean that you are sure about it. I have been stuck on this problem for a while and I need help!!

To determine whether the given sequence is arithmetic or geometric, we need to analyze the pattern of the numbers.

An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. In other words, each term is obtained by adding (or subtracting) the same value to the previous term.

A geometric sequence is a sequence in which the ratio between consecutive terms is constant. In other words, each term is obtained by multiplying (or dividing) the previous term by the same value.

Let's analyze the given sequence: 81, 3, 1/9, ...

To determine if it is arithmetic, we check if the difference between consecutive terms is constant. In this case, the difference between each term is not a constant value. Therefore, the sequence is not arithmetic.

To determine if it is geometric, we check if the ratio between consecutive terms is constant. In this case, the ratio between each term is indeed constant.

Let's calculate the ratio between each term:
3 / 81 = 1/27
1/9 / 3 = 1/27

As we can see, the ratio between consecutive terms is always 1/27. Therefore, the sequence is geometric.

The correct answer is B) The sequence is geometric because it decreases by a factor of 1/27.

81*(1/27)^n

what is that for n=1?
for n=2?