Question

10, 20, 40, 80, ...
find the common ratio for the geometric sequence.

Explanation:

Step1: Recall the formula for common ratio

In a geometric sequence, the common ratio \( r \) is found by dividing any term by its previous term, i.e., \( r=\frac{a_{n}}{a_{n - 1}} \).

Step2: Calculate the ratio using the first two terms

Take the second term \( a_{2} = 20 \) and the first term \( a_{1}=10 \). Then \( r=\frac{20}{10}=2 \). We can verify with other terms: \( \frac{40}{20} = 2 \) and \( \frac{80}{40}=2 \), so the common ratio is consistent.

Answer:

2