Question

What is the COMMON RATIO of the geometric sequence: 3024, 504, 84, 14, ...* 2

Answer 1

Answer:

$\frac{1}{6}$

Step-by-step explanation:

To find the common ratio of a geometric sequence, we  can divide one of the terms by the one before it

$r = \frac{u_n}{u_{n-1}}$

Let's try to apply that to the sequence in the question prompt:

$r = \frac{504}{3024}\\\\r = \frac{1}{6}$

The common ratio must be the same all throughout the sequence, so we can try this with two other values from the sequence just to be sure

$r = \frac{84}{504}\\\\r = \frac{1}{6}$

Now we can be sure that the common ratio of this geometric sequence is $\frac{1}{6}$

Note: $r$ is usually used to denote the common ratio

Good luck!