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
kipiarov [429]
3 years ago
5

what is the common ratio of the geometric sequence below? –96, 48, –24, 12, –6, ... a, -2 b,-1/2 c, 2 d, 1/2

Mathematics
2 answers:
marysya [2.9K]3 years ago
8 0

Answer:

Option b is correct.

The common ratio for the given geometric sequence is; \frac{-1}{2}

Step-by-step explanation:

The given sequence is;  -96, 48 , -24, 12 , -6, .....

Since, given sequence is Geometric

Geometric Sequence in which each term is found by multiplying the previous term by a constant(i.e common ratio)

In general we write geometric sequence as;

a , ar, ar^2, ar^3 , .....

where a be the first term and r is the common ratio.

On comparing the given sequence with general geometric sequence;

we get

a = -96                  ......[1]

ar = 48                   ......[2]

ar^2 = -24              .....[3]

and so on....        

To find the common ratio i.e, r;

Divide equation [2] by [1];

\frac{ar}{a} =\frac{48}{-96}

Simplify:

r = \frac{-1}{2}

Similarly,

by dividing the equation [3] by [2] we get;

\frac{ar^2}{ar} = \frac{-24}{48}

Simplify:

r = \frac{-1}{2}

As, you can see that the value of r is constant i.e, r= \frac{-1}{2} in the given sequence.

Therefore, the common ratio for the given geometric sequence is; r= \frac{-1}{2}


Georgia [21]3 years ago
5 0

The common ratio of the geometric sequence - 96,\,48, - 24,12, - 6, \ldots is \boxed{ - \frac{1}{2}}.

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.

The options are as follows,

(a). -2

(b). - \dfrac{1}{2}

(c). 2

(d). \dfrac{1}{2}

Explanation:

The first term of the geometric sequence is -96, second term of the geometric sequence is 48, third term -24, the fourth geometric sequence is 12 and the fifth term of the sequence is -6.

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

\begin{aligned}r&=\frac{{{a_2}}}{{{a_1}}}\\&= \frac{{48}}{{ - 96}}\\&=- \frac{1}{2}\\\end{aligned}

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

\begin{aligned}r&= \frac{{{a_3}}}{{{a_2}}}\\&= \frac{{ - 24}}{{48}}\\&= - \frac{1}{2}\\\end{aligned}

The common ratio of the geometric sequence - 96,\,48, - 24,12, - 6, \ldots is \boxed{ - \frac{1}{2}}.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

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.

You might be interested in
Evaluate f(−3) for f(x)=2x2−x+5.
Natasha2012 [34]

Answer: -4

Step-by-step explanation:

2(-3)*2-(-3)+5= -4

7 0
3 years ago
PLSSS HELPP I BEGG What is the solution to the system of linear equations graphed below?​
OleMash [197]

Answer:

No solution

Step-by-step explanation:

because the are parallel lines they never meet so they are inconsistent so there is no solution

8 0
3 years ago
Arranging like terms; solve the linear system using eliminationlly - 3x = 18- 3x = -16y + 33
DENIUS [597]

Solution

For this case we can do the following:

11y - 3x = 18

16y -3x = 33

We can multiply the first equation by -1 and we got:

-11y +3x =-18

16y -3x = 33

_______________

16y -11y = 33-18

5y = 15

y= 15/5 = 3

And then solving for x we got

x = -(18 -11*3)/ 3= -15/3 = 5

8 0
1 year ago
Help plsssssssssssssss
Darya [45]

Answer:

MNP is congruent to QST.

N = S.

Angle S is 78 degress

6 0
3 years ago
Read 2 more answers
Helpppppppppppppppppppppplppoooooo
Komok [63]

Answer:

hope it helps you plz mark me brilliantest

Step-by-step explanation:

B

6 0
3 years ago
Read 2 more answers
Other questions:
  • When a quadratic function is graphed, it will produce a parabola. Describe the difference between a Minimum Vertex and a Maximum
    14·1 answer
  • The Mulraney's home has 2,550 square feet of living space. A contractor is building an addition to their home that will increase
    9·2 answers
  • The height and radius are the same in both cylinders. Which cylinder has the greatest volume?
    11·1 answer
  • Is g(x)=-2f(x)+4 a vertical shift?
    7·1 answer
  • Black Lives Matter!!! <3
    14·2 answers
  • WILL MARK YOU BRAINLIEST
    7·2 answers
  • PLEASE ANSWER ASAP FOR BRAINLEST AND SHOW WORK!!!!!!!!!!!!!!!11
    14·1 answer
  • 40% of Michelles monthly earnings goes to her rent payment .If Michelle is paid 3200 every month, how much does she pay in rent?
    10·1 answer
  • Please help!<br> 31 = 11g
    13·2 answers
  • Help po plsss !!!!!!!​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!