Mathematics High School

What is the sum of the first eight terms of the geometric series 2 + 6 + 18 + 54+ ...? 510 3,280 6,560 4,374

Answers

Answer 1

Answer:

6,560

Step-by-step explanation:

Answer 2

Answer:

6,560

Step-by-step explanation:

We are given the first four terms of the sequence:

2, 6, 18, 54, ...

We need to find another four terms to find the sum.

I don't know how to explain how I got the pattern but you have to multiply by 3:

2 * 3 = 6

6 * 3 = 18

18 * 3 = 54

To find the next term, we will multiply 54 by 3:

54 * 3 = 162

2, 6, 18, 54, 162, ...

We now have 5 terms.

Next, multiply 162 by 3:

162 * 3 = 486

2, 6, 18, 54, 162, 486, ...

We now have 6 terms.

Next, multiply 486 by 3:

486 * 3 = 1458

2, 6, 18, 54, 162, 486, 1458, ...

We now have 7 terms.

Lastly, multiply 1458 by 3:

1458 * 3 = 4374

2, 6, 18, 54, 162, 486, 1458, 4374, ...

We now have the first 8 terms.

Now, we add all these numbers together:

2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 = 6560

The sum of the first eight terms of the geometric sequence is 6,560

Related Questions

Which are the partial products for 8x362? Select all that apply.

Answers

Answer:

Are you guys classmates?

1.A five - layer of cake weighs half a kilogram per layer.In each layer,the cake is decorated with icing which weighs 15g.3 candles which weighs 100g each is added.What is the total weight in kilogram of the fully decorated cake?​

Answers

Answer:  2.815 kilograms

======================================================

Work Shown:

1 layer = 0.5 kg

5 layers = 5*(0.5 kg) = 2.5 kg

icing = 15 g = 15/1000 = 0.015 kg

1 candle = 100 g = 100/1000 = 0.1 kg

3 candles = 3*(0.1 kg) = 0.3 kg

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

The five layers combine to 2.5 kg. On top of that we have 0.015 kg of icing, and then finally the three candles add 0.3 kg more weight.

The total weight is therefore: 2.5+0.015+0.3 = 2.815 kilograms

A phone company offers two monthly plans. Plan A costs $26 plus an additional $0.13 for each minute of calls. Plan B costs $17 plus an additional $0.18 for each minute of calls. Please help me!

Answers

Answer:

DSC

Step-by-step explanation:

I need help ASAP! I am offering brainiest to whoever answers the question first!

Answers

Answer:

Step-by-step explanation:

1536(4)(4)=24576

Answer:1536(4)(4)=24576

Step-by-step explanation:

The table shows the balance of an account each year.

Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account? What is the balance after 10 years?

Answers

Answer:

The interest rate is $2, the balance after 10 years will be $60.

Step-by-step explanation:

Each year the balance of the account increases by $2, so that would be the interest rate. After 10 years, the account will have 40 + 2 * 10 which equals $60.

At a real estate​ agency, an agent sold a house for ​$389,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is ​30% of the amount the real estate agency gets. How much did the agency make on the​ house? How much did the agent earn in​ commission?

Answers

Answer:

I fr don’t know

Step-by-step explanation:

Find the midpoint of the segment with the following endpoints.
(8,2) and (1,10)

Answers

Answer:

I am not sure but i think the midpoint is 4.5 and 6

Simplify the expression -1x-5(2x-y)-3y

Answers

Answer:

-11x + 2y

Step-by-step explanation:

when you go to answer this, can someone please give me the steps on how to do it, because I think I'm doing it wrong ​

Answers

Answer:

TUA=123

Step-by-step explanation:

so first we find <TUS in terms of x

so 180-11x-2

178-11x

so now we can use the sum of a triangle's angles which is always 180 to find the angles in triangle TUS

178-11x+5x+10+58=180

178-6x=112

take 178 from both sides

-6x=-66

x=11

so we can do 11x11+2=TUA

TUA=123

Pls help me this is due in 10 mins

Answers

3. .6 and 60%
4. 0.625 and 5/8
5.6/25 and 24%
6. .62 and 62%

8.40
9.9
10.60
11.70

How tall is a stack of 10 chairs?

5 chairs are 51 inches

3 chairs are 45 inches

8 chairs are 60 inches

Answers

Answer:

10 chairs are 102 inches

Step-by-step explanation:

Beacause 5 chairs are 51 so the double of chairs will be 102 inches

Sam bought 6 pens for an unknown price plus a
backpack. If he spent a total of $28.50, write an
equation to find the cost of each pen.

Answers

so sam bought SIX pens for a TOTAL of $28.50. we have to figure out how much money each of the six pens cost.

steps:

1. divide the total by the amount of items purchased:

28.50 / 6 = 4.75

and there’s your answer! each pen cost $4.75

steps to check your work:

1. multiply the single cost by the amount of items purchased:

4.75 ( 6 ) = 28.50

Answer the Following Question relating it to the mid-point theorem, with explanation.

Answers

Answer:

wait wouldnt it be "The second one"

Step-by-step explanation:

I dont wanna get you wrong but like wouldnt it Diagonals AC and BD are perpendicular I dont wanna get yo wrong!

Solve this system of equations.Write your answer as an ordered pair.3x+4y=36 y=-1/2x+8

Answers

Answer:

x = 4

y = 6

Step-by-step explanation:

[tex]\left \{ {{3x+4y=36} \atop {\frac{1}{2}x+4y=8 }} \right.[/tex] rewrite the equations and multiply bottom equations by -4

[tex]\left \{ {{3x+4y=36} \atop {-2x-4y=-32}} \right.[/tex] add both equations together

x = 4

then, input x=4 into equation 3x+4y=36:

3(4)+4y=36 (simplify)

12+4y=36 (subtract 12 from both sides)

4y=24 (divide both sides by 4)

y=6

Angle ABC is a straight angle. The measure of angle ABD is x. What is the value of x?

Answers

Answer:

45 degrees

Step-by-step explanation:

A straight angle is equal to 180, so subtract 135 from 180

Answer:

45

Step-by-step explanation:

Need help ASAP
Thankss + BRAINLIST only for correct answer

Answers

Answer(5,6)

Step-by-step explanation:

Pensé un número, a ese
número le sumé 15 y
obtuve como resultado 27.
¿Cuál es el número que
pensé​

Answers

Answer:

si es suma tiene que ser 12+15=27

Kim got 82%, 75%, and 74% on the first 3 tests.
What grade does she need on the 4th test to have an average of 80% on all 4 tests?
A. 77%
B. 80%
O c. 85%
D. 89%
E. 100%

Answers

Answer:

C

Step-by-step explanation:

Add all percentages together, then divide by how many you added.

Answer:

C

Step-by-step explanation:

The fisherman pays a contractor to repair his dock. The charges are $1200 for lumber, $60 for sales tax, and $750 for labor. The fisherman pays $260 down and finances the remainder. There is a finance charge of $41.06.

Answers

Answer:

Im guessing we have to add these, considering you did not put the rest of the question. In that case, the answer would be 2311.06

Step-by-step explanation:

Is the point (3, 11) a solution for the linear equation 1/3x + y = 12? Explain.

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

The point is on the line.

The coordinate values satisfy the equation:

  1/3x + y = 12

  1/3(3) + 11 = 12 . . . substitute for x and y

  1 + 11 = 12 . . . . . . . true

Any point that satisfies the equation is a solution. (3, 11) is a solution.

Intro to slope-intercept form What is the y-intercept of the line represented by y = -6x – 11? Choose 1 answer: А (0, -6 B (0, -11) (-6,0) D (-11,0) Check About


pls help i suck at math​

Answers

Answer:

d

Step-by-step explanation:

B. it’s not D because (-11,0) is along the x-axis not the y-axis.

what type of polygon is this​

Answers

Answer:

enneagon

Step-by-step explanation:

Nonagon :) that’s bc of the nine sides in the polygon

Simplify
(x + 3)^8
(x + 3)^5

Answers

Answer:

1. Expand the expression.

x^8+24x^7+252x^6+1512x^5+5670x^4+13608x^3+20412x^2+17496x+6561

2. (x+3)^5

Use the Binomial Theorem.

x^5+5x^4⋅3+10x^3⋅3^2+10x^2⋅3^3+5x⋅3^4+3^5

Simplify each term.

x^5+15x^4+90x^3+270x^2+405x+243

Step-by-step explanation:

hope it is helpful....

Answer:

42x

Step-by-step explanation:

hakim wrote an equation to represent the number of meters he would run for each kilometer, k, in a long distance race.W hat is the value of k if 1,000k =0?​

Answers

k=500 because of the kilometer

Round 13,649 to the nearest thousand

Answers

Answer:

14,000

Step-by-step explanation:

13,649

the 6 in the hundredths place rounds up therefore the 3 in the thousands place turns into a 4

-12 + 2t = - 14
Solve for t

Answers

Answer:

-1

Step-by-step explanation:

-12 + 2t = -14

12 + -12 + 2t = -14 + 12

2t = -2

2t/2 = -2/2

t = -1

OOPS my submitted answer was wrong.

Submitting this is so you can give other person points! :]

Mario has 160 pizzas and is collecting two pizzas a week. Write the equation for the number of pizzas Mario has

Answers

Answer:

160+2x

Step-by-step explanation:

Answer:

Mario has after 5 weeks 170 pizzas.

Step-by-step explanation:

Each time add to the chart 2 Pizzas and move a week.

If a rectangle measures 21 centimeters by 28 centimeters what is the length in centimeters of the diagonal of the rectangle

Answers

Answer:

35cm

Step-by-step explanation:

Given data

Length= 21cm

Width= 28cm

Diagonal= ???

Applying Pythagoras theorem

D^2= L^2+W^2

D^2= 21^2+28^2

D^2= 441+784

D^2= 1225

D= √1225

D= 35cm

Hence the diagonal is 35cm

Evaluate the expression when y=6 and x=9.
x+7y

Answers

Answer:

9+(7)(6)

9+42=51

Step-by-step explanation: hope this help

Help me pls ty :D
助けてください

Answers

Answer: Me don’t know

Step-by-step explanation:

65%

Step-by-step explanation:

130000/200000*100=65%

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