Given the first term $A_1 = \frac{1}{8}$ and the recursive formula $A_n = \frac{1}{4} \times A_{n-1}$, we can determine the subsequent terms in the sequence.

Let's break it down:

Formula:

$A_n = \frac{1}{4} \times A_{n-1}$

Sequence Calculation:

1. First term: $A_1 = \frac{1}{8}$

2. Second term $(A_2)$: $A_2 = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}$

3. Third term $(A_3)$: $A_3 = \frac{1}{4} \times \frac{1}{32} = \frac{1}{128}$

4. Fourth term $(A_4)$: $A_4 = \frac{1}{4} \times \frac{1}{128} = \frac{1}{512}$

Sequence:

The complete sequence is: $\frac{1}{8}, \frac{1}{32}, \frac{1}{128}, \frac{1}{512}, \dots$

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the sequence change if the formula was $A_n = \frac{1}{2} \times A_{n-1}$?
2. What is the general form of the nth term for this sequence?
3. How would you sum the first four terms of this sequence?
4. How does changing the constant factor in the formula impact the sequence’s growth rate?
5. Can this sequence be represented as a geometric series?

Tip: Recursive sequences are defined by relating each term to the previous one. Understanding the formula helps in predicting the entire sequence.