Solve.
-For the geometric sequence 64, 16, 4, 1, ... , find a

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with a common ratio of $\frac{1}{4}$. To find the 11th term, we can use the formula $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Plugging in, we get:
$$a_{11} = 64 \cdot \left(\frac{1}{4}\right)^{10} = \frac{64}{4^{10}} = \frac{64}{2^{20}}$$
Simplifying, we get:
$$\frac{64}{2^{20}} = \frac{2^6}{2^{20}} = 2^{-14}$$
Converting to scientific notation, we get $2^{-14} = 1.52587890625 \cdot 10^{-5}$. Therefore, the 11th term is approximately $1.52587890625 \cdot 10^{-5}$.
Since only choice A is equal to $1.52587890625 \cdot 10^{-5}$, it must be the correct answer.

Solve. -For the Geometric Sequence 64, 16, 4, 1,