The fourth term in an arithmetic sequence is 18 and the seventh term is 39. If the first term is a1 , which is an equation for the nth term of this sequence?

Answers

Answer 1

Answer:

           aₙ = 7n - 10

Step-by-step explanation:

The nth term:  [tex]a_n=a_1+d(n-1)[/tex]

So:

    a₄ = a₁ + 3d

18 =  a₁ + 3d   ⇒   3d =  18 - a₁

    a₇ = a₁ + 6d

39 = a₁ + 6d

39 = a₁ + 2(18 - a₁)

39 = a₁ + 36 - 2a₁

39 = 36 - a₁

a₁ = -3

3d = 18 - (-3)

3d = 21

d = 7

So the nth term:

                            [tex]a_n = -3 + 7(n-1)\\\\a_n=-3 +7n - 7\\\\a_n = 7n - 10[/tex]


Related Questions

A local bakery called Brianny's makes 100 batches of cookies in 4 hours. If they keep this pace, how many batches of cookies would they make in 16 hours?

Answers

Answer:

400 batches of cookies

Step-by-step explanation:

4 hours = 100 cookies

8 hours = 200 cookies

12 hours = 300 cookies

16 hours = 400 cookies

If the number of students who participated in art decreased by 5, how many total students would the principal have expected in order to keep the number of students who participated in art proportional to the total number of students surveyed? ​

Answers

Answer: There isn’t enough context.?

Step-by-step explanation:

using long division what is 238 divided by 11

Answers

Answer:

21

7 Remainder

Step-by-step explanation:

1 1 ⟌ 2 3 8

 0    

 1 1 ⟌ 2 3 8

0    

 1 1 ⟌ 2 3 8

      0    

 0    

 1 1 ⟌ 2 3 8

     - 0    

       2    

       0    

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

       0 2  

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

0 2  

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

       2 2  

       0 2  

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

     - 2 2  

         1   0 2  

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

     - 2 2  

         1 8

0 2 1

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

     - 2 2  

         1 8

       0 2 1

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

     - 2 2  

         1 8

         1 1

       0 2 1

 1 1 ⟌ 2 3 8

     - 0    

       2 3  

     - 2 2  

         1 8

     -   1 1

           7

238 divided by 11 equals 21 with a remainder of 7.

To divide 238 by 11 using long division, we follow these steps:

Set up the division: Write 238 as the dividend and 11 as the divisor. Place the dividend inside the long division symbol and the divisor outside of it.

Begin dividing: Divide the first digit of the dividend (2) by the divisor (11). The quotient is 0 since 2 is less than 11.

Bring down the next digit of the dividend (3) and place it after the 0. We now have 23.

Divide 23 by 11. The quotient is 2 as 11 goes into 23 two times.

Multiply the divisor (11) by the quotient (2) and subtract the result from 23:

23 - (11 x 2) = 23 - 22 = 1

Bring down the next digit of the dividend (8). We now have 18.

Divide 18 by 11. The quotient is 1 as 11 goes into 18 one time.

Multiply the divisor (11) by the quotient (1) and subtract the result from 18:

18 - (11 x 1) = 18 - 11 = 7

There is no more digit to bring down, so we have completed the division. The final remainder is 7.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ6

Marcy’s breakfast table has a square table top with an area of 36 square feet. What is the approximate diagonal length of the table top? Round to the nearest tenth.

Answers

Answer:

8.5 ft = length of diagonal

Step-by-step explanation:

If A = 36 ft^2, then s (length of one side) = 6 ft.

The diagonal and any one side create a 45 degree angle.  

sin 45 degrees = (length of side opposite the 45 degree angle)/hypotenuse

                                                          6 ft            6√2 ft          

Then (length of hypotenuse) = ------------------ = ---------------

                                                      sin 45 deg            1

This works out to 8.5 ft = length of diagonal

Venus and Arian went berry picking. Venus picked 3 1/3 buckets of berries and Arian picked up 5 4/5 buckets. How many buckets of berries do they have altogether? If they need 11 full buckets, how many more buckets of berries do they need?

Answers

Answer: 9.13333333333

3 1/3+ 5 4/5=

Answer#2  1.86666666667

There plz help me I still have one more

Answers

Answer:

D.

5/5 is basically 1 whole number :)

Simplify: -(14x)0y(-7)z

Answers

-14x*0*-7z

0y=0
-(14x)=-14x

NEED HELP I WILL BE GIVING BRAINLIEST:)

Answers

Answer:

mathematics

Step-by-step explanation:

The number of blueberry muffins made is 40% of the total number of total muffins they make daily.

On tueday, the baker makes 60 muffins. How many miffins does the Baker bakes on Tuesday?​

Answers

The answer to your question is:

24

Answer:

probably 24

Step-by-step explanation:

WHAT DOES THIS MEAN GIMME THE ANSWER

Answers

Answer:

This is a geometric sequence and the ratio is equal to 4.

Step-by-step explanation:

Arithmetic means you can continue the sequence through addition or subtraction.

Geometric means you can continue the sequence through multiplication or division.

To get from 3 to 12, we could either add 9 (arithmetic) or multiply by 4 (geometric).

To get from 12 to 48, we could either add 36 or multiply by 4.

Since we are looking for a pattern, the sequence would be geometric. This is because the sequence can be continued by multiplying by 4 each time. It cannot be arithmetic because we cannot add by 9 each time.

On a side note, common difference is used when describing arithmetic while ratio is used to describe geometric.

A principal gathered data about the distance, in miles, that his teachers and bus drivers live from the school. The box plots below show these data. Based on the box plots, which statement is true? *

well i think is C or D

Answers

Answer:

Step-by-step explanation:

It is C

What is i30
A. 1
B. -i
C. -1
D. i

Answers

c) -1 is the answer to this question
C.-1 is the correct answer :)

If we had the equation x+4=14, what would we do to get x by itself

Answers

Answer:

Subtract 4 from both sides

Step-by-step explanation:

x+4=14

-4 -4

x=10

Answer:

substract 4 from both sides of the equation

Step-by-step explanation:

so we have x + 4 = 14

how can we get x?

We can get x by simply substracting 4 from both sides:

x + 4 = 14  => x = 10

and now we can tell, that the x is 10, easy right?

How do I find the next four of the sequence?

Answers

Step-by-step explanation:

In this arithmetic sequence, the common difference d is 7. You can find this by subtracting a term from the consecutive term: 16 - 9 = 7, 23 - 16 = 7. In order to find the next four terms, keep adding 7 to the previous term. The next four terms are 30, 37, 44, and 51.

Answer:

Step-by-step explanation:

[tex]a_{1}[/tex] = [tex]\frac{3}{4}[/tex]

d = - [tex]\frac{1}{4}[/tex]

[tex]a_{2}[/tex] = [tex]\frac{3}{4}[/tex] + ( - [tex]\frac{1}{4}[/tex] ) = [tex]\frac{1}{2}[/tex]

[tex]a_{3}[/tex] = [tex]\frac{1}{2}[/tex] - [tex]\frac{1}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

[tex]a_{4}[/tex] = - [tex]\frac{1}{2}[/tex] - [tex]\frac{1}{4}[/tex] = - [tex]\frac{3}{4}[/tex]

[tex]a_{5}[/tex] = - [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{4}[/tex] = - 1

Use the distributive property to simplify the expressions.

1. b(6 + 5b)
2. 4( n + 5)

Answers

Answer:

Step-by-step explanation:

Ok i can help

1. Step 1

b(6 + 5b)  Apply distributive property

b*6+b*5b

Step 2

b*6+b*5b  Multiply

6b+5bb

Step 3

6b+5bb

6b+5b^2

Answer

6b+5b^2

2 Step 1

4( n + 5)  Apply distributive property

4n+4*5

Step 2

4n+4*5  Multiply the numbers

4n+20

Answer

4n+20

hope this helps

Help T_T ill give brainlist

Answers

Answer:

See below.

Step-by-step explanation:

The domain and range are correct.

The relation is a function because no x value is used more than once.

The area of a right triangle is 12 cm2. Which of the following could be the lengths of the legs of the triangle?

2 cm and 6 cm
4 cm and 6 cm
3 cm and 2 cm
3 cm and 4 cm

Answers

Answer:

6 and 4

Step-by-step explanation: since it is "cm2" it means it was already halved. This means that the answer was originally 24, 6x4 is the only one that equals 24.

easy algebra question below first correct answer gets brainliest, if you put one of those links you will get reported and blocked

Answers

Answer:

15^2 = 8^2 + x^2 = 12.69.

Step-by-step explanation:

Find the circumference of the given circle

Answers

Answer:

18.84

Step-by-step explanation:

Circles and i neeeeed help

Answers

Answer:

60 degrees

Step-by-step explanation:

Using the 172 degrees and calculating it's distance from the angle, i conclude that it's 60

9514 1404 393

Answer:

  (b)  60

Step-by-step explanation:

The external angle is half the difference of the two subtended arcs.

  x° = (172° -52°)/2 = 120°/2

  x° = 60°

The value of x is 60.

3 Which ordered pair is the solution for this
system of linear equations?
2x + y = 6
5x + 3y = 14

A (-2, 10)
B (4,-2)
C (1,3)
D (3,0)

Answers

Answer is : B (4,-2) .

Which value of x makes the inequality -* < 8 true?
A
X = 32
B
X = 35
x = 34
D
= 2

Answers

Answer:

D: x = 2

Step-by-step explanation:

Go down the multiple choices answers and plug each value in for x until the inequality is true:

A:

1/4(32) < 8

1/4 × 32/1 < 8

32/4 < 8

8 < 8

8 is not less than 8 so this is false (8 = 8).

B:

1/4(35) < 8

35/4 < 8

8 3/4 < 8

8 3/4 is not less than 8 so this is false (8 3/4 > 8).

C:

1/4(34) < 8

34/4 < 8

8 2/4 < 8

8 2/4 is not less than 8 so this is false (8 2/4 > 8).

D:

1/4(2) < 8

2/4 < 8

2/4 is less than 8 so this is true (2/4 = 1/2 = 0.5 > 8).

Helppp, 60 points!!!

Answers

Answer:

the answer is c

Step-by-step explanation:

please mark this answer as brainliest

Answer:

The answer is c

Step-by-step explanation:

By moving 5 units to the right you lend at x-1 y-3

8 yd
6 yd
15 yd
10 yd
Answer:




please help!:)

Answers

Answer:

What's the question???

Step-by-step explanation:

A and b are positive integers and a-b=2. Evaluate the following:
(27^1/3b)/ ( 9^1/2a)

(this is urgent)

Answers

Answer:
a) 1/27
b) 1
c) 125
Step-by-step explanation:
a) (9^(0.5b))/(3^a)
(3²)^(0.5b) ÷ (3^a)
(3^b) ÷ (3^a)
3^(b - a)
a - b = 3
b - a = -3
3^(-3)
1/27
b) (27^(1/3b)) /(9^(0.5b))
(3³)^(b/3) ÷ (3²)^(0.5b)
(3^b) ÷ (3^b)
1
c) ( 125^(1/3a))/(25^(1/2b))
(5³)^(a/3) ÷ (5²)^(b/2)
5^a ÷ 5^b
5^(a - b)

125

Number 6 please help 10 points

Answers

Answer: The graph would have 4 bars

Step-by-step explanation: The graph would have 4 bars because there are 4 numbers

HALP ME PLZZ ASAP NO LINKS

Answers

Answer:

Step-by-step explanation:

Please help I will give brainliest

Answers

Answer:

option 1 is equivalent to 3^2.3^5

Answer: A.) 3^10 / 3^3

What are the three theorems we can use
to show that two triangles are similar? Draw
an example of each theorem using two
triangles.
10th grade LT1

Answers

Answer:

Hope this will help you....

Please help asap oiuytyghjkjhugytfhjkl

Answers

Answer:

112

Step-by-step explanation:

correct me if im wrong.

I got this from doing 30 percent out of 160

160×0.30

160-48=112

Answer:

112

Step-by-step explanation:

30%*160=48

160-48=112

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