Question

Find the 8th term in the following geometric sequence.

28, 14, 7, 3.5, . . .

Answer 1

[AI-generated answer — Bot GPT 3.5]

We notice that each term is half of the previous term. The common ratio is $\frac{1}{2}$, so the 8th term is $\left(\frac{1}{2}\right)^{8-1} \times 28 = \boxed{0.5}$.

Answer 2

are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the error in my previous response. I mistakenly stated that the common ratio is $\frac{1}{2}$ when it is actually $\frac{1}{2}$. Let's try again.

The first term of the sequence is 28 and the common ratio is $\frac{1}{2}$. To find the 8th term, we can use the formula for the nth term of a geometric sequence:

$$a_n = a_1 \cdot r^{n-1}$$

In this case, $a_1 = 28$ and $r = \frac{1}{2}$. Plugging in the values, we have:

$$a_8 = 28 \cdot \left(\frac{1}{2}\right)^{8-1}$$
$$a_8 = 28 \cdot \left(\frac{1}{2}\right)^7$$
$$a_8 = 28 \cdot \frac{1}{128}$$
$$a_8 = \frac{28}{128}$$
$$a_8 = \boxed{\frac{7}{32}}$$

Therefore, the 8th term in the sequence is $\frac{7}{32}$.