All categories

2 years ago

Find the common ratio of the geometric sequence 18,-72,288,...

Mathematics

1 answer:

tamaranim1 [39]2 years ago

5 0

Answer:

<em>The common ratio of the geometric sequence is -4</em>

Step-by-step explanation:

<u>Geometric Sequence</u>

A geometric sequence is defined as a series of numbers that follow a fixed pattern: Each term equals the previous term times a fixed number called the common ratio. The recursive formula is:

$a_n=a_{n-1}*r$

Where r is the common ratio.

We are given three terms of a geometric sequence:

18,-72,288,...

To find the common ratio, just divide each term by the previous term:

$\displaystyle r=\frac{-72}{18}=-4$

Make sure it's a fixed number and test with the third term:

$\displaystyle r=\frac{288}{-72}=-4$

Since both numbers coincide, the common ratio of the geometric sequence is -4

You might be interested in

A plane takes off from an airport and flies at a speed of 400km/h on a course of 120° for 2 hours. the plane then changes its co

butalik [34]

Answer:

Distance from the airport = 894.43 km

Step-by-step explanation:

Displacement and Velocity

The velocity of an object assumed as constant in time can be computed as

$\displaystyle \vec{v}=\frac{\vec{x}}{t}$

Where $\vec x$ is the displacement. Both the velocity and displacement are vectors. The displacement can be computed from the above relation as

$\displaystyle \vec{x}=\vec{v}.t$

The plane goes at 400 Km/h on a course of 120° for 2 hours. We can compute the components of the velocity as

$\displaystyle \vec{v_1}=$

$\displaystyle \vec{v_1}=\ km/h$

The displacement of the plane in 2 hours is

$\displaystyle \vec{x_1}=\vec{v_1}.t_1=.(2)$

$\displaystyle \vec{x_1}=km$

Now the plane keeps the same speed but now its course is 210° for 1 hour. The components of the velocity are

$\displaystyle \vec{v_2}=$

$\displaystyle \vec{v_2}=km/h$

The displacement in 1 hour is

$\displaystyle \vec{x_2}=\vec{v_2}.t_2=.(1)$

$\displaystyle \vec{x_2}=km$

The total displacement is the vector sum of both

$\displaystyle \vec{x_t}=\vec{x_1}+\vec{x_2}=+$

$\displaystyle \vec{x_t}=km$

$\displaystyle \vec{x_t}=$

The distance from the airport is the module of the displacement:

$\displaystyle |\vec{x_t}|=\sqrt{(-746.41)^2+492.82^2}$

$\displaystyle |\vec{x_t}|=894.43\ km$

8 0

3 years ago

You and 4 of your friends want to make some soup for lunch each person would like to eat 1 1/3 cup soup how many cups of soup wi

Pavlova-9 [17]

Multiply the amount of people by the amount of cups they want

4*1 1/3=5 1/3
You would have to make 5 and 1/3 cups of soup

Hope this helps!

4 0

2 years ago

Read 2 more answers

I didn’t learn about this can you help me with this

arlik [135]

If you're taking trig, the "sum and difference formulas for trig functions" are basic facts that you'll need to learn and commit to memory. I'd suggest you look up these formulas on the net. You will likely immediately find listings for the sine, cosine and tangent.

5 0

3 years ago

A mailing carton in the shape of a cube has a volume of 684 cubic inches. What is the length of one side of the carton to the ne

Liula [17]

Check the picture below.