# Given the geometric sequence: 4,24,144, .... What is the common ratio?

Jan 6, 2017

the common ratio is 6

#### Explanation:

The common ratio is obtained by calculating ${a}_{n + 1} / {a}_{n}$

that's

$\frac{24}{4} = \frac{144}{24} = \frac{864}{144} = 6$

Jan 6, 2017

6

#### Explanation:

The ${n}^{t h}$ term of a geometric sequence is generated by:

${a}_{n} = {a}_{\text{n-1}} \times r$
Where r is the common ratio

In this example: ${a}_{0} = 4$

${a}_{1} = 24 = {a}_{0} \times 6$

${a}_{2} = 144 = {a}_{1} \times 6$

.. and similarly for ${a}_{3}$

Hence: The common ratio $r = 6$