Question

Look at the following sequence:1/3 3/12 9/48 27/192If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose "not geometric."

Answer 1

For finding if its a geometric sequence, we will do the quotient between a value of the sequence and the one before it. If we obtain the same number, this will be the common ratio.

For the terms 1 and 2:

$\frac{\frac{3}{12}}{\frac{1}{3}}=\frac{9}{12}=\frac{3}{4}=0.75$

For the terms 2 and 3:

$\frac{\frac{9}{48}}{\frac{3}{12}}=\frac{9\cdot12}{3\cdot48}=\frac{108}{144}=\frac{54}{72}=\frac{27}{36}=\frac{9}{12}=\frac{3}{4}=0.75$

For the terms 3 and 4:

$\frac{\frac{27}{192}}{\frac{9}{48}}=\frac{27\cdot48}{192\cdot9}=\frac{3\cdot48}{192}=\frac{3\cdot24}{96}=\frac{24}{32}=\frac{12}{18}=\frac{3}{4}=0.75$

Finally, as all quotients give the same number, we conclude that the initial sequence is a geometric one, and that its common ratio is 0.75.