What is the common ratio, r, for the sequence represented by the formula an = 3(2)^-n?

1/2
2
3
6
Is it 2?

The nth term has 2^-n, so the ratio is 2^-1 = 1/2

Did you try listing the first few terms? That would have made it clear that 2 was not the ratio.

1/2

To find the common ratio (r) for the sequence represented by the formula an = 3(2)^-n, we need to compare two consecutive terms.

Let's find the ratio between the terms aₙ and aₙ₊₁:

aₙ = 3(2)^-n
aₙ₊₁ = 3(2)^-(n+1)

To find the ratio, r, we divide the second term by the first term:

r = aₙ₊₁ / aₙ = (3(2)^-(n+1)) / (3(2)^-n)

Simplifying this expression:

r = (3(2)^-(n+1)) / (3(2)^-n)
= (3 * 2^-(n+1)) / (3 * 2^-n)
= 2^-(n+1 - (-n))
= 2^-(n+1+n)
= 2^-(2n+1)
= 1 / (2^(2n+1))
= 1 / (2 * 2^n)
= 1/2 * 1 / 2^n
= (1/2)^(n+1)

Therefore, the common ratio (r) for the sequence represented by the formula an = 3(2)^-n is (1/2)^(n+1).

So, the correct answer is 1/2, not 2.

To find the common ratio, r, you need to compare two consecutive terms in the sequence. In this case, the sequence is represented by the formula an = 3(2)^-n.

Let's calculate the values of the sequence for the first few terms:

a1 = 3(2)^-1 = 3/2
a2 = 3(2)^-2 = 3/4
a3 = 3(2)^-3 = 3/8

Now, we can find the ratio between consecutive terms:
a2 / a1 = (3/4) / (3/2) = (3/4) * (2/3) = 1/2

Since the ratio between consecutive terms is 1/2, the common ratio, r, for the sequence represented by the formula an = 3(2)^-n is indeed 1/2.

Therefore, the correct answer is 1/2, not 2.