Question

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

Answer 1

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

Answer 2

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.