Mathematics, 13.10.2019 17:20 RoyalGurl01

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

Answers: 3

Show answers

Answers

Answer from: genyjoannerubiera

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; $r= \frac{-1}{2}$

Answer from: gabbycasey102

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).

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

(c).

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

Explanation:

The first term of the geometric sequence is , second term of the geometric sequence is 48, third term , 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 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:

Learn more about inverse of the function Learn more about equation of circle Learn more about range and domain of the function

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 from: Quest

9.8? i'm not really sure

Answer from: Quest

The answer of the question is x=0 and y= $\frac{8}{5}$

Another question on Mathematics

Mathematics, 21.06.2019 18:00

When lulu enlarged her drawing of a rabbit, the enlarged picture appeared to be distorted. which statement about the transformation applied to her drawing is true?

Answers: 2

Answer

Mathematics, 21.06.2019 18:10

The means and mean absolute deviations of the individual times of members on two 4x400-meter relay track teams are shown in the table below. means and mean absolute deviations of individual times of members of 4x400-meter relay track teams team a team b mean 59.32 s 59.1 s mean absolute deviation 1.5 s 245 what percent of team b's mean absolute deviation is the difference in the means? 9% 15% 25% 65%

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

Aremote-controlled boat can travel at 4 feet per second in calm water. the boat traveled 48 feet with the current, and then it traveled 16 feet against the current in the same amount of time. how fast is the current?

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

What is the period of the sinusoidal function ?

Answers: 3

Answer

You know the right answer?

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

Questions

Mathematics, 11.03.2021 04:50

What is the area of the triangle in the coordinate plane? 108 units² 91 units² 54 units² 44 units²