1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elis [28]
3 years ago
7

Here are the first four terms of a sequence.

Mathematics
1 answer:
Nataly_w [17]3 years ago
8 0

Answer:

  • aₙ = 2n² + n + 1

Step-by-step explanation:

We observe that the difference of terms is 4, 7 and 15 and next level difference is 4. It means the sequence is quadratic.

<u>We can compare this with simple quadratic sequence </u>

  • 1, 4, 9, 16

<u>and find out that doubling each term gives us </u>

  • 2, 8, 18, 32

This is close to our sequence, write the terms as follows to find exact rule

<u>The first term: </u>

  • a₁ = 4  = 2*1² + 2 = 2*1² + 1 + 1

<u>The second term</u>

  • a₂ = 11  = 2*2² + 3 = 2*2² + 2 + 1

<u>The third term:</u>

  • a₃ = 22 = 2*3² + 4 = 2*3² + 3 + 1

<u>The fourth term:</u>

  • a₄ = 37 = 2*4² + 5 = 2*4² + 4 + 1

<u>The nth term as per observation above is:</u>

  • aₙ = 2n² + n + 1
You might be interested in
Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long. If the hook is 5 meters from
bagirrra123 [75]

Answer:

12 meters

Step-by-step explanation:

Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.

From Pythagoras theorem;

c^2 = a^2 + b^2

a^2= c^2 - b^2

a= √c^2-b^2

From the question

c= 13 metres

b= 5 metres

a= the unknown

a= √c^2-b^2

a= √(13)^2 - (5)^2

a= √169 - 25

a= √144

a= 12 meters

6 0
3 years ago
Read 2 more answers
Find the distance between the two points in simplest radical form HELP​
GaryK [48]

Given:

The two points on the graph.

To find:

The distance between the two points in simplest radical form.

Solution:

From the given graph, it is clear that the two points on the graph are (-9,3) and (-3,-2).

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using the distance formula, the distance between two points (-9,3) and (-3,-2) is:

d=\sqrt{(-3-(-9))^2+(-2-3)^2}

d=\sqrt{(-3+9)^2+(-5)^2}

d=\sqrt{(6)^2+(-5)^2}

On further simplification, we get

d=\sqrt{36+25}

d=\sqrt{61}

Therefore, the distance between the given points is \sqrt{61} units.

7 0
3 years ago
You randomly choose a letter A, and do not replace it. Then, you choose another letter A. What is the probability that both lett
GarryVolchara [31]
You made the choice to choose the letter A, a second time.
3 0
3 years ago
Will give brainliest!!!!!!! Please help I need correct answer!!!
andreyandreev [35.5K]

Answer:

The answer is "was the first time the Constitution defined what a citizen is"

does this help?

8 0
2 years ago
Read 2 more answers
What does b represent in the equation of a line in the form y = mx + b?
timama [110]
B is the y intercept.
7 0
3 years ago
Read 2 more answers
Other questions:
  • The penguins won 5 out of 8 preseason games. If their the same through 82 regular season games, about have many regular season g
    9·1 answer
  • Determine the range of the function.
    12·1 answer
  • Lauren's suv was detected exceeding the posted speed limit of 60 kilometers per hour, how many kilometers per hour would she hav
    14·1 answer
  • Two angles are supplementary. One angle is 80 degrees. What is the value of the other angle? please hurry
    11·2 answers
  • Which angle is an inscribed angle
    8·2 answers
  • Person A can paint the​ neighbor's house 3 times as fast as Person B. The year A and B worked​ together, it took them 10 days. H
    10·1 answer
  • What is the answer to 5+1×10?
    11·2 answers
  • How do you dilate a figure when the center of dilation is NOT the origin?
    10·1 answer
  • Write this in a Algebraic expression. (Use x as your variable) The sum of x squared and y
    8·1 answer
  • un tipo de bacteria se duplica cada 6 minutos.¿ cuántas bacterias habia en un comienzo si luego de una hora hay 2048?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!