Answer:
The common ratio is [tex]\frac{1}{4}[/tex]
The next term in the sequence is 2
Step-by-step explanation:
In a geometric sequence, the common ratio is the constant value you multiply a term by in order to find the value of the following term. Therefore, it is mathematically calculated as the quotient between a term and the term immediately before it. And it is in fact That is:
common ratio [tex]r=\frac{a_{n+1}}{a_n}[/tex]
This quotient should be true for any two consecutive terms in the sequence.
so using the first two terms, we find:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{a_{2}}{a1}=\frac{128}{512} =\frac{1}{4}[/tex]
You can test that this common ratio is true for all other terms listed:
[tex]\frac{a_3}{a_2} =\frac{32}{128} =\frac{1}{4} \\\frac{a_4}{a_3} =\frac{8}{32} =\frac{1}{4} \\[/tex]
So now, in order to find the term that follows, all we need to do is to multiply the last term given (8) by this common ratio:
[tex]a_5=8*\frac{1}{4} =2[/tex]
