1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Naddika [18.5K]
3 years ago
10

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

Mathematics
2 answers:
Komok [63]3 years ago
7 0

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.

Crazy boy [7]3 years ago
6 0

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}



You might be interested in
Select 3 ratios that are equivalent to 8:20​
guapka [62]

Answer:

4:10, 2:5 16:40

Step-by-step explanation:

just multiply or divide

5 0
3 years ago
Find the area under the standard normal curve between z=0.45 and z=1.13
Law Incorporation [45]

Step-by-step explanation:

the answer is in the above image

8 0
3 years ago
A builder buys bricks at the rate of $4.50 per brick for the first 10, $3.50 per brick for the next 10, and $2.50 for any additi
iogann1982 [59]
If the first 10 bricks come out at $ 4.5, I would be spending $ 45. The other 10 bricks come out at $ 3.5 so he would be spending $ 35. Therefore, he has $ 20 available to buy bricks at $ 2.5, which would be buying 8 additional bricks. Thus, in total, with $ 100, 28 bricks were purchased.

8 0
2 years ago
What is the length (magnitude) of the vector (2,-1)?
KiRa [710]

Answer:

\[\sqrt{5}\]

Step-by-step explanation:

The given vector is represented by (2,-1).

This can be represented in general form as (x,y) where x=2 and y=-1.

Magnitude of the vector represented as (x,y) is given by [\sqrt{x^{2}+y^{2}}\]

Evaluating for the given values of x and y,

\[\sqrt{2^{2}+(-1)^{2}}\]\[=\sqrt{4+1}\]

\[=\sqrt{5}\]

Length of the vector is \[\sqrt{5}\]

5 0
2 years ago
Pls help asap
VMariaS [17]

Answer: Addition

Step-by-step explanation: You can represent that as 10^5*10^-5

If you add the exponent values, you get 10^0 which is equal to 1. If you multiply them, you get 10^-25 which is wrong.

3 0
2 years ago
Read 2 more answers
Other questions:
  • sally and martha had the same number postcards. after sally sold 18 of her postcards, martha had 4 times as many postcards as sa
    11·1 answer
  • A map of Brasilia has a scale of 1 inch to 5 miles. If the city is 2 7/16 inches across on the map, what is the distance across
    6·1 answer
  • When a person agrees to a regular, fixed payment of wages over a period of time, he/she agrees to earn a
    5·2 answers
  • Line AB contains points A (−6, 3) and B (2, −5). Line AB has a slope that is
    5·2 answers
  • What is the solution (x, y) to the system of equations shown?
    7·1 answer
  • Answer the question in the picture?
    6·1 answer
  • Please help i’ll give brainliest
    5·1 answer
  • Square root of 45 minus square root of 5
    14·2 answers
  • Larry wants to purchase birthday gifts for his twin sisters. One sister likes daises which costs $2.00 per stem and the other li
    15·1 answer
  • Decide which story can be represented by the system of equations below.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!