please answer this question​

Please Answer This Question

Answers

Answer 1

Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

[tex]a_n[/tex] is the nth term[tex]a[/tex] is the first term[tex]d[/tex] is the common difference between terms

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

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

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]


Related Questions

A nickel has a diameter of 21.21 millimeters. What is the area of the face of a nickel? Use 3.14 for π . Round to the nearest hundredth if necessary.

Answers

The area of the face of a nickel 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

What is Area of Circle?

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

As the surface of nickel is in shape of 2-D circle.

radius of circle = [tex]\frac{21.21}{2}[/tex] = 10.605 mm

Area of circle= [tex]\pi r^{2}[/tex]

                      = 3.14* 21.21*21.21

                      = 353.143 [tex]mm^{2}[/tex]

                      = 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

Thus, the area of the face of a nickel 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

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You pick a card at random.
6
7
8
9
What is P(less than 7)?
Write your answer as a fraction or
whole number.

Answers

The answer to your question is 6


A bookstore had 120 copies of a magazine. Yesterday the bookstore sold
of these copies. How many copies were sold yesterday?
Write your answer in simplest form.

Answers

Answer:

120

Step-by-step explanation:

120 copies sold yesterday

How can you find out the similarities and differences in a non-fiction text?
A. look at how the characters speak
B. look at how the subject or events are portrayed
C. look at the genre

Answers

The similarities and differences in a non-fiction text look at how the subject or events are portrayed.

What is a non-fiction text?

Comparing non-fiction texts can focus on the similarities between the texts - things they have in common. You can also contrast texts and focus on their differences - things that set the texts apart from each other. You could compare and contrast the following:

Form – What types of text (letter, news report, etc) are they?

Purpose – What job (persuading, informing, advertising) is each text doing?

Audience – Who is the intended reader of the text?

Subject matter – What are the texts about?

Language choices – What kinds of words, images or rhetorical devices are being used?

Structure – How is the text ordered?

Tone – What is the overall tone or mood of the writing?

Non-fiction texts are all around us, and comparing them can help you become more aware of how language is being used in society. Comparing non-fiction texts can often prompt you to notice things that you might not have considered about a text in isolation.

Hence the similarities and differences in a non-fiction text look at how the subject or events are portrayed.

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what is the slope intercept of 3x-2y=-16.

Answers

                 - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

          What is the slope-intercept form of 3x-2y=-16?

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

✥ First, we need to subtract 3x on both sides, which results in

-2y=-16-3x

Or

-2y=-3x-16

[tex]\bigstar[/tex] Now, divide by -2 on both sides:-

[tex]\bold{(-2y):-2=(-3x-16):-2}[/tex]

On simplification,

[tex]\bold{y=\dfrac{3}{2} x+8}[/tex]

Good luck with your studies.

          - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Please help me ojn this question

Answers

Answer: r = 1.5

Step-by-step explanation:

The geometric sequence formula is in the attached image.

Using the formula, we take number 3, which is 9.

[tex]9 = 4(r)^{2} \\\frac{9}{4} = r^{2} \\\sqrt{\frac{9}{4}} = 1.5[/tex]

1. Find the value of x in this figure.

Answers

Answer:

x = 30º

Step-by-step explanation:

Let's call the midpoint of OP, R.

The triangle of OQR would be an equilateral triangle since OQ = OR as they are both radii and is OQR and ORQ are 60º, ROQ is also 60º, making the triangle equilateral. Because tangents meet a circle at 90º, the angle RQP would be 30º and since angles on a straight line add to 180º, the angle QRP would be 180-ORQ which is 120º. Now we know the 2 angles in triangle of QRP so we can work out the final angle since angles in a triangle add to 180º. So:

180 - 120 - 30 = 30º.

x = 30º

This would also prove that QR and RP are the same since base angles in an isosceles triangle are equal.

What is the value of x in the equation 1/5x - 2/3y = 30, when y = 15?
A. 4
B. 8
C. 80
D. 200

Answers

200

Step-by-step explanation:

1/5x -2/3y =30

Plug in 15 for y.

x-(15)= 30

2/3x of 2/3(15) is 10.

1/5x -10-30

Add 10 to each side.

1/5x = 40

Divide each side by 1/5.

(dividing by a fraction is the same as multiplying by its reciprocal...flip 1/5...*5)

x=200

Please help explain, tyy

Answers

Answer:

3. (3, 6)
4. (3, 7)
5. (3, 36)

Step-by-step explanation:

These are slope functions, so there's is no definite answer for x as it tells you to solve when x is 3. So put simply lets do that. Knowing that x is now 3, we can solve for all the functions. This will give you y, which is f(x) which just tells you the equations represents a function or slope on a graph. All these equations create lines. Solving for question 3, 3 + 3 is 6, so f(x) = 6, and the answer is (3, 6). For 4, you do 3 x 3 - 2, which is 9 - 2 = 7. So (3, 7). So on and so forth.

Solve for x and y. The triangles in each pair are similar​

Answers

Answer:

x=13.69

Step-by-step explanation:

154/30=5.13

33*5.13

plugin

13.69

which expression is equivalent
to -14 - 35 d please help for 50 points

Answers

Answer:

number 1

Step-by-step explanation:

the first one on the left

Which of these is an exponential parent function?

Answers

Did you provide an picture ?!

All-purpose carpeting costs $27.50 per square meter. What is the cost of carpeting a room from
wall to wall whose dimensions are 360 centimeters × 400 centimeters?

Answers

Step-by-step explanation:

I'm not sure if I got the correct answer since English is not my first language

A 2-pack of movie tickets costs $17.24. What is the unit price

Answers

Answer:

As the two pack of ticket cost 17.24. Mean that the unit or the price of one pack will be half of it which is

8.62

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

Given ,

2 pack movie tickets costs $17.24

Unit price = $17.24/2 = $8.62

What is the volume of a rectangular prism with the dimensions: base 238 cm, height 113 cm, and length 334 cm?

Answers

Answer: 8,982,596 cm

Step-by-step explanation:

Rectangular Prism Volume = Height * Length * Width/base

238 cm * 113 cm * 334 cm = 8,982,596 cm

Spinner A and Spinner B below are each to be spun once.

If the pointer CANNOT land on a line, how many different outcomes of a number and a color are possible?

18
12
9
6

Answers

Answer:

9

Step-by-step explanation:

Spinner A = 6 outcomesSpinner B = 3 outcomes6 + 3 = 9

Math question help pls

Answers

Answer:

the circumference of the circle is 50.24

Please help me guys

a) If 2 Tan a = 3 Tan B, then show that Tan (a-B) =5 sin2b/5Cos 2B-1

Answers

Given that :-

2 tan A = 3 tan B

Prove that :-

Tan (a-B) = [ sin 2B/(5 – cos 2B)]

Taking RHS :-

= sin 2B/(5 – cos 2B)] = [(2 tan B)/(1 + tan2B)]/ [5 – {(1 – tan2B)/(1 + tan2B)}]

= (2 tan B)/ [5(1 + tan2B) – 1 + tan2B]

= (2 tan B)/[5 + 5 tan2B – 1 + tan2B)

= (2 tan B)/(4 + 6 tan2B)

= (2 tan B)/[2(2 + 3 tan2B)]

= tan B/(2 + 3 tan B tan B)

Dividing the numerator and denominator by 2,

= [(1/2) tan B]/ [1 + (3/2) tan B tan B]

= [(3/2) tan B – tan B]/[1 + tan A tan B] {from (i)}

= (tan A – tan B)/(1 + tan A tan B)

= tan(A – B) = LHS

What statement is NOT true comparing the two
box and whisker plots?

Answers

Answer:

Its d

Step-by-step explanation:

Can someone help me with this please?

Answers

The final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

What are matrices?

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns in mathematics.

The calculation of the given matrix is as follows:-

[tex]\rm D-C= \left[\begin{array}{ccc}13&2&-5\\6&-4&0\\\end{array}\right] - \left[\begin{array}{ccc}1&4&-8\\3&-5&2\\\end{array}\right] \\[/tex]

[tex]\rm D-C= \left[\begin{array}{ccc}(13-1)&(2-4)&(-5+8)\\(6-3)&(-4+5)&(0-2)\\\end{array}\right][/tex]

[tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

Hence the final matrix will be as follows   [tex]\rm D-C=\left[\begin{array}{ccc}12&-2&3\\3&1&-2\\\end{array}\right][/tex]

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pls help what is the m ACD?

Answers

Answer:

Angle ACD = 54° ( Angle standing on same arc at the circumference are equal )

A Student was conducting as to determine how many house g apples could be packed in al bay Size at the local farmers. The average gala apples had a Of 3.5 inches. Given the farmer's market wanted to use a box that had the dimensions 16 in x 9in x 9in how many apples should fit based on the information provided by the table. (a) 30 (b) 35 (c)40 (d)
20in × 13in ×12in= 72 apples
12in × 12in × 12in= 40 apples
20in × 10in × 6in= 28 apples

Answers

Answer:

43.1

Step-by-step explanation:

1728/40 = 43.2

3120/72 = 43.3

Find the surface area

Answers

Answer:

should be 872 in^2

Step-by-step explanation:

Answer:

Area = 872

Step-by-step explanation:

Formula for the surface area of a rectangular prism is

A=2(wl+hl+hw)

Plug in

A =2·(8·17+12·17+12·8)=872

In how many ways can we stack 10 books?

Answers

The arrangement of items can be done with the use of permutation. The stacking of the number of books in the question can be done in 3,628,800 ways.

The arrangement of a given number of items can be done when definite numbers are to be considered at once by the use of permutation. A permutation is a mathematical method that can be used to determine the number of ways by which given items are to be arranged in a particular order.

Given that 10 books are to be stacked, the number of ways (n) that this can be done can be determined by:

n = 10!

  = 10 x 9 x 8 x7 x6 x5 x4 x3 x2x 1

n = 3,628,800

Therefore, the 10 books can be stacked in 3,628,800 ways.

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Please help me out!

Answers

Answer:

it is the there'd one

if this is wrong sorry

PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL

Answers

your answer would be 147°

solution:

since ∠x and ∠y are supplementary angles. they must add up to 180°

so ∠+∠y=180°

     ∠x=180°-∠y

     = 180°- 33°

=147

Mrs. Forsyth has 130 pieces of candy. She wants to split it into fifths for each of her classes. How
many pieces of candy will each class get?

Answers

Answer: The answer is 26

I just divided it by 5

Answer: 26
Explanation: 130/5 = 26

find g(-3) g(2) g(4)

Answers

g(-3) = 0.5 =

[tex] \frac{1}{2} [/tex]

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

g(2) as defined = 2

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

g(4)= 8-4 = 4

what is the interquartile range of the data 24,25,27,36,37,42,42,43,49,49,50,53,59,61,65

Answers

IQR = Q3-Q1 = 53 - 36 = 17

A 12 _ foot ladder is leaning against a house the ladder reaches 7.7 feet up the wall wha is the angle of elevation of the ladder?

Answers

Check the picture below.

Make sure your calculator is in Degree mode.

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