Mathematics: Pleaseee help asap easyy

The common ratio of the geometric sequence is Further Explanation: If the first term a and the second term ar is known then, the value of r can be obtained as follows, The nth term of the geometric sequence can be obtained as, Given: The geometric sequence is The options are as follows, (a). (b). (c). (d). 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 The...

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Ответ:

dre2544

12.07.2020

Mathematics

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.

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