All categories

3 years ago

Which of the following is a geometric sequence?

Mathematics

2 answers:

LuckyWell [14K]3 years ago

7 0

Geometric sequences use either division or multiplication as the common ratio. The third choice down has a common ratio of 3. 1*3=3, 3*3=9, 3*9=27, etc.

marin [14]3 years ago

7 0

Answer:

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.

You might be interested in

What is the probability that there is at most one purple marble? 0.100 0.301 0.770 0.971

andriy [413]

The probability that there is at most one purple marble is 0.9701.

<h3>What is the probability about?</h3>

Probability is a term that connote the possibility of an event or something occurring or not.

Note that it is one that is based on the level of occurrence that can be seen in a random event.

Based on the fact that there is a bag that has eight yellow marbles, nine green marbles, three purple marbles, and five red marbles, the probability that there is at most one purple marble is 0.9701.

Learn more about This probability case from

brainly.com/question/3729438

#SPJ4

3 0

2 years ago

Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

Jobisdone [24]

Parameterize $S$ by the vector function

$\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k$

so that the normal vector to $S$ is given by

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}$

In this case, the normal vector is

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k$

with magnitude $\sqrt{1^2+2^2+1^2}=\sqrt6$ . The integral of $f(x,y,z)=e^z$ over $S$ is then

$\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx$

where $T$ is the region in the $x,y$ plane over which $S$ is defined. In this case, it's the triangle in the plane $z=0$ which we can capture with $0\le x\le8$ and $0\le y\le\frac{8-x}2$ , so that we have

$\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}$

5 0

3 years ago

BRAINLIEST ASAP for BRAINLIEST!!! <br> EASY MATH! Do with explanation

natulia [17]

Step-by-step explanation:

you plug 0 into the (x,y) into the equation. if your finding x you plug in 0 for y and versa.

so y = 9x -3 im going to find x

0 = 9x -3 subtract -3 from both sides

-3 = 9x divide by 9

x = -3

4 0

3 years ago

Really confusing......

valina [46]

Answer:

She spent 40 more dollars or to be exact 40.70 dollars more then aiden

Step-by-step explanation:

Aiden bought 60 candles.

0.37*60 is equal to $22.20

Aidens sister bought 170 candles at same price of $0.37

0.37*170=$62.90

Now subtract

$62.90-22.20=$40.70

She spent 40 more dollars or to be exact 40.70 dollars more then aiden

4 0

2 years ago

Read 2 more answers

Solve a" + 14a + 45 = 0 by factoring

pantera1 [17]

Answer:

a = -3

Step-by-step explanation:

-3 + (14 * -3) + 45 = 0

-3 + -42 + 45 = 0

-3 + 3 = 0

So, the answer is -3

Hope this helps! :)

3 0

3 years ago