Question

what is the next term of the geometric sequence?
128, 32, 8, \boxed{}

Explanation:

Step1: Find the common ratio

In a geometric sequence, the common ratio \( r \) is found by dividing a term by its previous term. Let's take the second term divided by the first term: \( r=\frac{32}{128}=\frac{1}{4} \). We can check with the third term divided by the second term: \( \frac{8}{32}=\frac{1}{4} \), so the common ratio \( r = \frac{1}{4} \).

Step2: Calculate the next term

To find the next term (the fourth term) in a geometric sequence, we use the formula \( a_{n}=a_{n - 1}\times r \), where \( a_{n-1} \) is the previous term and \( r \) is the common ratio. Here, \( a_{3}=8 \) and \( r=\frac{1}{4} \), so the next term \( a_{4}=8\times\frac{1}{4}=2 \).

Answer:

2