Question

find the next term of the sequence:

\\(\frac{1}{1}, \frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \frac{1}{256}, \square\\)

Explanation:

Step1: Identify the sequence type

The sequence is geometric with a common ratio.

$$r = \frac{\frac{1}{4}}{\frac{1}{1}} = \frac{1}{4}$$

Step2: Calculate the next term

Multiply the last term by the common ratio.

$$\frac{1}{256} \times \frac{1}{4} = \frac{1}{1024}$$

Answer:

\(\frac{1}{1024}\)