Question

5) Find the common ratio and the next term. 512, 128, 32, 8,

Answer 1

Answer:

The common ratio is $\frac{1}{4}$

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 $r=\frac{a_{n+1}}{a_n}$

This quotient should be true for any two consecutive terms in the sequence.

so using the first two terms, we find:

$r=\frac{a_{n+1}}{a_n}=\frac{a_{2}}{a1}=\frac{128}{512} =\frac{1}{4}$

You can test that this common ratio is true for all other terms listed:

$\frac{a_3}{a_2} =\frac{32}{128} =\frac{1}{4} \\\frac{a_4}{a_3} =\frac{8}{32} =\frac{1}{4}$

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:

$a_5=8*\frac{1}{4} =2$