Question

Find the common ratio. Write the answer in lowest terms. 8+12+18+27+...

Answer 1

Answer:

$r=\dfrac{3}{2}$

Step-by-step explanation:

Consider the sequance

$a_1=8\\ \\a_2=12\\ \\a_3=18\\ \\a_4=27\\ \\...$

Note that

$\dfrac{a_2}{a_1}=\dfrac{12}{8}=\dfrac{3}{2}\\ \\ \\\dfrac{a_3}{a_2}=\dfrac{18}{12}=\dfrac{3}{2}\\ \\ \\\dfrac{a_4}{a_3}=\dfrac{27}{18}=\dfrac{3}{2}\\ \\...$

So, common ratio is

$r=\dfrac{3}{2}=1\dfrac{1}{2}$