Question

What is the common ratio for the geometric sequence? 32, 8, 2, 12, ... Enter your answer in the box.

Answer 1

Answer:

Given sequence is not a geometric progression and there will be no common ration for this sequence.

Step-by-step explanation:

Need to determine common ration for the following geometric sequence

32, 8, 2, 12, ...

In given geometric sequence  

a1 = 32, a2=8, a3=2, a4=12 ……….

Common ratio = $\frac{a_2}{a_1} =\frac{a_3}{a_2} =\frac{a_4}{a_3}$

$\frac{a_2}{a_1}=\frac{8}{32}=\frac{1}{4}$

$\frac{a_3}{a_2} =\frac{2}{8}=\frac{1}{4}$

$\frac{a_4}{a_3}=\frac{12}{2}=6$

Since $\frac{a_2}{a_1}=\frac{a_3}{a_2}\neq\frac{a_4}{a_3}$  so we can say that given sequence is not a geometric progression and there will no no common ration for this sequence.