Question

what is the common ratio for the geometric sequence below, written as a fraction? 768, 480, 300, 187.5, …

Answer 1

The common ratio of the geometric sequence $768,480,300,187.5, \ldots$ is $\boxed{\frac{5}{8}}.$

Further Explanation:

If the first term a and the second term ar is known then, the value of $r$ can be obtained as follows,

$\boxed{r = \frac{{{a_2}}}{{{a_1}}}}$

The nth term of the geometric sequence can be obtained as,

$\boxed{{a_n} = a \times {r^{n - 1}}}$

Given:

The geometric sequence is $768,480,300,187.5, \ldots.$

Explanation:

The first term of the geometric sequence is 768, second term of the geometric sequence is 480, third term 300 and the fourth geometric sequence is 187.5.

The common ratio $r$ between the second and first term can be obtained as follows.

$\begin{aligned}r&=\frac{{{a_2}}}{{{a_1}}}\\&= \frac{{480}}{{768}}\\&= \frac{5}{8}\\\end{aligned}$

The common ratio r between the second and third term can be obtained as follows.

$\begin{aligned}r&= \dfrac{{{a_3}}}{{{a_2}}}\\&=\dfrac{{300}}{{480}}\\&= \dfrac{5}{8}\\\end{gathered}$

Hence, the common ratio of the geometric sequence $768,480,300,187.5, \ldots$ is $\boxed{\frac{5}{8}}.$

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometric progression

Keywords: geometric sequence, fraction, written as, common ratio, first term, second term, sum of geometric sequence, 768, 480, 300, 187.5.

Answer 2

Let

$a1=768\\a2=480\\a3=300\\a4=187.5$

Step $1$

Find $\frac{a2}{a1}$

$\frac{a2}{a1} =\frac{480}{768}$

Divide by $96$ numerator and denominator

$\frac{480}{768} =\frac{\frac{480}{96}}{\frac{768}{96}} \\ \\ \frac{480}{768}=\frac{5}{8}$

$a2=a1*\frac{5}{8}$

Step $2$

Find $\frac{a3}{a2}$

$\frac{a3}{a2} =\frac{300}{480}$

Divide by $60$ numerator and denominator

$\frac{300}{480} =\frac{\frac{300}{60}}{\frac{480}{60}} \\ \\ \frac{300}{480}=\frac{5}{8}$

$a3=a2*\frac{5}{8}$

Step $3$

Find $\frac{a4}{a3}$

$a4=187.5 \\ a4=187\frac{1}{2} \\ \\ a4=\frac{375}{2}$

$\frac{a4}{a3} =\frac{\frac{375}{2}}{300} \\ \\ \frac{a4}{a3} =\frac{375}{600}$

Divide by $75$ numerator and denominator

$\frac{375}{600} =\frac{\frac{375}{75}}{\frac{600}{75}} \\ \\ \frac{375}{600}=\frac{5}{8}$

$a4=a3*\frac{5}{8}$

In this problem

The geometric sequence formula is equal to

$a(n+1)=a(n)*\frac{5}{8}$

For $n\geq 1$

therefore

the answer is

the common ratio for the geometric sequence above is $\frac{5}{8}$