Here are the first four terms of a sequence.
4
11
22
37
Find an expression, in terms of n, for the nth term of this sequence.

Answers

Answer 1

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.

We can compare this with simple quadratic sequence

1, 4, 9, 16

and find out that doubling each term gives us

2, 8, 18, 32

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

The first term:

a₁ = 4  = 2*1² + 2 = 2*1² + 1 + 1

The second term

a₂ = 11  = 2*2² + 3 = 2*2² + 2 + 1

The third term:

a₃ = 22 = 2*3² + 4 = 2*3² + 3 + 1

The fourth term:

a₄ = 37 = 2*4² + 5 = 2*4² + 4 + 1

The nth term as per observation above is:

aₙ = 2n² + n + 1
Answer 2

Answer:

Step-by-step explanation:


Related Questions

The number of pledges that Melissa collected for this year's charity walk is 8 less than half the number of pledges she collected last year. Which expression represents the number of pledges she collected this year?

Answers

Answer:

1/2x - 8

Step-by-step explanation:

Let

x = number of pledges she collected last year

The number of pledges that Melissa collected for this year's charity walk is 8 less than half the number of pledges she collected last year.

Number of pledges she collected this year = 1/2x - 8

The expression which represents the number of pledges she collected this year = 1/2x - 8

How do you write 96,000 in scientific notation?

Answers

Answer: 96,000 is an even five-digits composite number following 95999 and preceding 96001. In scientific notation, it is written as 9.6 × 10⁴.

Answer:

96 K

Step-by-step explanation:

step 1 : Start counting the decimal places from zero to six , as they are three and that would be [tex]10^3[/tex] which's equal to kilos

the quotient of b and 2?

Answers

Answer:

b ÷ 2 or b/2

Step-by-step explanation:

Quotient means division which is represented by "÷" or "/".

b ÷ 2 or b/2

Best of Luck!

Based on the definition of logarithm, explain why log10 100 = 2.

Answers

The base of the log is the number and what it is equal to is the exponent. 10^2 is 100.
Does that make sense?

y = -2 +4.
y = 2x - 5
Plot two lines by clicking the graph.
Click a line to delete it.

Answers

Answer:

y=2

x=7/2

Step-by-step explanation:

can anyone please help me:)​

Answers

Answer:

sorry i don't know the answer but i have Nicholas sage

Step-by-step explanation:

Select the correct answer.

Which equation represents the line that is parallel to y = 3 and passes through (-2,-8)?
ОА. x= -2
OB. x= 3
OC. y=-8
OD. y= 3x-2

Answers

Answer:

its answer C. y=-8

Step-by-step explanation:

y=-8 passes through (-2, -8) and is parallel to y=3 because they're both horizontal

The equation represents the line that is parallel to y = 3 and passes through (-2,-8) is,

⇒ y = -8.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have given that,

The line that is parallel to y = 3 and passes through (-2,-8)

Now, We have to determine the parallel line passes through (-2,-8)

Slope of line y = 3 is, 0.

So, the slope of the line parallel to y = 3 is also 0.

Thus, the equation of line passes through (-2,-8) and parallel to y = 3 is,

y - (- 8) = 0(x - (-2))

y = - 8

Thus, The equation represents the line that is parallel to y = 3 and passes through (-2,-8) is y=-8.

To learn more about the equation of the line visit:

brainly.com/question/18831322

#SPJ5

how to simplify arithmetic explicit formulas to general linear form?

an= 7+5(n-1) as an example

Answers

Answer:

an = 5n + 2

Step-by-step explanation:

an = 7 + 5(n - 1)

an = 7 + 5n - 5

an = 5n + 2


ONLY NEED PART B HELP


The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8:6. Terrence owns 36 model
cars.
Part A
How many model cars does Jim own?
Part B
Will the ratio change if Jim and Terrence each sell ten of their model cars? Explain.

Answers

Answer: 48 model cars

Step-by-step explanation: 1. You know that the ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 4:3.

2. Let's call the number of model cars that Jim owns is , therefore, you can solve the exercise as following:

3. Therefore, Jims owns 48 model cars.

Simplify -15.5/5.
The first answer gets brainliest :]

Answers

Answer:

-3.1

Hope this helps

Answer:

-3.1

Step-by-step explanation:

Division

What is the percent of change from 40 to 58?

Answers

Answer:

45 percent

Step-by-step explanation:

Answer:

36%

Step-by-step explanation:

First, subtract 58-40. That equals 18. Now, divide 18 by 50. When doing division, you get the answer 0.36. Lastly, multiply it by 100. Moving the decimal place, you get 36%.

write down the first three terms of the sequence whose nth term is given by 2n-5

Answers

Answer:

- 3, - 1, 1

Step-by-step explanation:

To find the first 3 terms substitute n = 1, 2, 3 into the formula

a₁ = 2(1) - 5 = 2 - 5 = - 3

a₂ = 2(2) - 5 = 4 - 5 = - 1

a₃ = 2(3) - 5 = 6 - 5 = 1

The first 3 terms are - 3, - 1, 1

Can someone read and answer the question please ?

Answers

Answer: the last one

Step-by-step explanation:

What is the slope of the line passing through the points
(0, – 5) and (4, 2)
?
What is the slope?

Answers

Answer:

7/4

Step-by-step explanation:

Please help :) Please and thank you :D

Answers

Answer I think the first one

Step-by-step explanation:Hope this helps

72 POINTS PLEASE HELP ME OR I WILL GET IN TROUBLE
Solve the following equation by showing all steps.

3 ( x – 2 ) = 15
Start by using distributive property:

Answers

Answer:

x=7

Step-by-step explanation:

distributive property: multiply both terms in the parentheses by the term outside the parentheses (3)

3 times x = 3x

3 times -2= -6

3x-6=15

move -6 to other side by adding 6+15

3x=21

divide 21 by 3

x=7

Answer:

x=7

Step-by-step explanation:

Evalute to 3x-6=15, then add 6 to both sides. Then, divide 3 by both sides to get x by itself getting you a answer which becomes, x=7.

A jewelry maker has 51 inches of chain. She wants to cut the chain into 9 equal parts. How long will each part be?

Answers

The 9 pieces of chain will be around 5.6 inches

Answer:

5.6 inches

Step-by-step explanation:

i only need help on number 9. Find the value of Y. ​

Answers

6y+40=10y-32
8=4y
Y=2

5. Write an equation in slope-intercept form of the line that
passes through the points (4, 6) and (4, 2).

Answers

Answer:

2

Step-by-step explanation:

True or false if two parallel lines are cut by a transversal each pair of corresponding angles are congruent

Answers

Answer:

False

Step-by-step explanation:

Help i’ll give 20 points

Answers

Answer:

d

Step-by-step explanation:

12 x 1.5 = 18

18 x 1.5 = 27

it is 1.5 bigger than the original rectangle

but its enlarged so nothing changes

Answer:

C. 20 by 32

Step-by-step explanation:

i had this question like a year ago and this was the answer i got from brainly. u just add 8 to each side so they stay proportionately similar

Grace is playing a game with her friend. They put the four balls shown into a container.
They take turns closing their eyes and pulling a ball from the container. Grace goes first.
What is the probability that Grace will pull out a striped ball?

Answers

Answer:

1/4

Step-by-step explanation:

because there are four balls therefore 1 out of 4 is going to be the answer

Tsits Cat
Quadrilateral problems on the
Please help!
coordinate plane
You are graphing Rectangle ABCD in the coordinate plane. The following are three of the vertices of the
rectangle: A(3,5), B(3,-4), and C(-2,-4).
What are the coordinates of point D?

Answers

Answer:

the trinagne

Step-by-step explanation:

000059.23 - 000044.18 =

Answers

Answer:

15.05

Step-by-step explanation:

Also, you don't need to add the zeros, they don't mean anything.

PLZ HELP ILL MARK BRAINLEST
The standard equation of a circle with center (h, k) and a vertical axis of symmetry is (x - h)² + ( y - k)² =r² A circle's center is (3,- 2) and the radius is 12. Which equation models the circle?
A)(x - 3) ² + (y + 2) ² = 12

B)(x + 3) ² = (y + 2) ² = 12

C) (x - 3) ² = (y + 2) ² = 144

D)(x + 3)² – ( - 2) ² = 144

Answers

NOTES: The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

THE ANSWER IS A

Rewrite to the algebraic form The product of x and 4.​

Answers

Answer:

4x

Step-by-step explanation:

When multiplying a number by a variable the number is written first and then the variable. It can be represented like this: 4(x). If you simplify that you get 4x.

Answer:

x=4

Step-by-step explanation:

he has driven 15 miles so far which is three-fifths of the way home what is the total length of his drive

Answers

Answer:

**The total length of his drive is 25 miles

Step-by-step explanation:

15 = 3/5

therefore 5 miles is 1/5 of the way home

15+5+5=25

What is the area of a right triangle 2 centimeters
high with a base of 4 centimeters?
ASAP NO EXPLAINING MARKING BRAINLIEST OMG PLSSSS

Answers

Answer:

4cm²

Step-by-step explanation:

plz help me solve the quadratic formula by factoring!!!!

m (m-3) = 0​

Answers

Answer:

m^2 - 3m = 0

Step-by-step explanation:

m(m-3) = 0

m^2 - 3m = 0

M=3 because m-3=0 and it is a logical equation

how do you undo dilation?

Answers

Currently there is nothing available for reversal of dilation. People who get dilated will still need to wear their sunglasses and to put off reading for a couple of hours until the effects of the dilation drops wear off.
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