Question

question
find the common ratio of the geometric sequence 19, 171, 1539, …

Explanation:

Step1: Recall common ratio formula

For a geometric sequence, the common ratio $r = \frac{a_n}{a_{n-1}}$, where $a_n$ is the $n$-th term and $a_{n-1}$ is the previous term.

Step2: Calculate using first two terms

Take $a_2=171$ and $a_1=19$.
$r = \frac{171}{19}$

Step3: Simplify the expression

$\frac{171}{19} = 9$

Step4: Verify with next pair

Check $a_3=1539$ and $a_2=171$: $r = \frac{1539}{171}=9$, which confirms the ratio.

Answer:

9