Mathematics, 16.07.2019 01:30 izzyisawesome5232

Which of the following is a geometric sequence?

Answers: 1

Show answers

Answers

Answer from: greg9207

Option C. 1,3,9,27, ... is a geometric sequence in which the common ratio is 3.

Step-by-step explanation:

In geometric sequence, the the ratio between two consecutive numbers is the same.

Now, consider the first case. The given sequence is $1, \dfrac{1}{2},\dfrac{1}{6}, \dfrac{1}{24}, ...$ .

In the above sequence, The ratios between consecutive numbers are:

$\dfrac{1}{2}:1=\dfrac{1}{2}\\\dfrac{1}{6}:\dfrac{1}{2}=\dfrac{1}{3}$

So, the ratio between two consecutive numbers is not the same and hence, it is not a geometric sequence.

Now, consider the second case. The given sequence is -1,-1,1,-1,-1,1, ... .

In the above sequence, The ratios between consecutive numbers are:

$-1:-1=1\\1:-1=-1$

So, the ratio between two consecutive numbers is not the same and hence, it is not a geometric sequence.

Now, consider the third case. The given sequence is 1,3,9,27, ... .

In the above sequence, The ratios between consecutive numbers are:

$3:1=3\\9:3=3\\27:9=3$

So, the ratio between two consecutive numbers is the same and hence, it is a geometric sequence.

Now, consider the fourth case. The given sequence is 3,6,9,12,... .

In the above sequence, The ratios between consecutive numbers are:

$6:3=2\\9:6=\dfrac{3}{2}$

So, the ratio between two consecutive numbers is not the same and hence, it is not a geometric sequence.

Therefore, option C. 1,3,9,27, ... is a geometric sequence in which the common ratio is 3.

For more details, refer the link:

link

Answer from: 20stirltrer

Option C. is the geometric sequence.

Step-by-step explanation:

In a geometric sequence there should be a common ratio in each successive term.

Now we will check the common ratio in each option.

A). $1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}........$

In this sequence if we find the common ratio

Ratio of second and first term = $\frac{\text{Second term}}{\text{First term}}$

= $\frac{\frac{1}{2}}{1}=\frac{1}{2}$

Similarly ratio of third and second term = $\frac{\text{Third term}}{\text{Second term}}$

= $\frac{\frac{1}{6}}{\frac{1}{2}}$

= $\frac{2}{6}$

= $\frac{1}{3}$

Here ratios are not common. Therefore, sequence is not a geometric sequence.

B). -1, -1, 1, -1, -1..............

ratio of second and first term = $\frac{-1}{-1}=1$

ratio of third and second term = $\frac{1}{-1}=-1$

Ratios are not equal so sequence is not a geometric sequence.

C). 1, 3, 9, 27...............

ratio of second and first term = $\frac{3}{1}=3$

ratio of third and second term = $\frac{9}{3}=3$

Both the ratios are same therefore, sequence is geometric.

D). 3, 6, 9, 12..............

ratio of second and first term = $\frac{6}{3}=2$

ratio of third and second term = $\frac{9}{6}=\frac{3}{2}$

Ratios are not equal so sequence is not a geometric sequence.

Answer from: Quest

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:40

Jonathan pays $1.90 per pound for potatoes. he buys 8.3 pounds of potatoes. he determines that he will pay $15.77, before tax, for the potatoes. which best describes the reasonableness of jonathan’s solution? jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product. jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product. jonathan’s answer is reasonable because is 16, and 16 is close to 15.77. jonathan’s answer is unreasonable because is 8, and 8 is not very close to 15.77.

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

Add the two expressions 3.8b - 7 and 2.9b + 9 enter your answer in simplified form

Answers: 1

Answer

Mathematics, 21.06.2019 17:40

A. 127 cm^2 b. 144.5 cm^2 c. 172 cm^2 d. 50 cm^2

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

For what values of the variable x is the expression square root of 7x+14+ square root of 7-x a real number?